A baseball (m=140g) traveling 32m/s moves a fielders
glovebackward 25cm when the ball is caught. What was the average
forceexerted by the ball on the glove?

Answer:

h2 = 0.092m

Explanation:

From a balance of energy from point A to point B, we get speed before the collision:

[tex]m1*g*h-\frac{m1*V_B^2}{2}=0[/tex]  Solving for Vb:

[tex]V_B=\sqrt{2gh}=6.56658m/s[/tex]

Since the collision is elastic, we now that velocity of bead 1 after the collision is given by:

[tex]V_{B'}=V_B*\frac{m1-m2}{m1+m2} = \sqrt{2gh}* \frac{m1-m2}{m1+m2}=-1.34316m/s[/tex]

Now, by doing another balance of energy from the instant after the collision, to the point where bead 1 stops, we get the distance it rises:

[tex]m1*g*h2-\frac{m1*V_{B'}^2}{2}=0[/tex] Solving for h2:

h2 = 0.092m

Answer:

Inverted

Real

Explanation:

u = Object distance =  30 cm

v = Image distance

f = Focal length = 10 cm

Lens Equation

[tex]\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{f}-\frac{1}{u}=\frac{1}{v}\\\Rightarrow \frac{1}{v}=\frac{1}{10}-\frac{1}{30}\\\Rightarrow \frac{1}{v}=\frac{1}{15}\\\Rightarrow v=15\ cm[/tex]

As, the image distance is positive the image is real and forms on the other side of the lens

[tex]m=-\frac{v}{u}\\\Rightarrow m=-\frac{-15}{30}\\\Rightarrow m=-0.5[/tex]

As, the magnification is negative the image is inverted

By applying the lens equation, we calculate that the image is formed 15 cm behind the lens. This is a real image as it forms on the opposite side of the lens, and in the case of a converging lens, it will be inverted.

First, we use the lens equation, which is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. In this case, the object distance 'do' is 30cm and the focal length 'f' is 10cm. Solving for 'di', we find that the image is located 15 cm behind the lens (i.e., on the opposite side from the object).

Since the image forms on the opposite side of the lens from where the object is, this indicates it's a real image. A positive image distance indicates a real image and a negative image distance indicates a virtual image.

For a converging lens, a real image is always inverted, and a virtual image is always upright. Therefore, in this case, the image would be inverted.

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Answer:

average and instant

Explanation:

The average speed is the ratio of the total path traveled and the time it took to travel that path, that is why the first space must be average speed, this because it takes into account the total amount of distance, and the total amount of time.

Instant speed, is the speed an objet (in this case a car) has in a particular moment in time, for this speed it doesn't matter the distance or the time that the car has traveled, it only matters the speed in that moment, that is what the speedometer measures, thus the second blank space must be instant speed.

To locate the emergency landed plane, we add the vectors representing the plane's two separate legs, breaking them into components using trigonometry. Summing these vectors gives us the direct path for the rescue crew in terms of both distance and bearing from the airport to the plane.

To assist in this emergency landing scenario, we need to compute the resulting position vector by analyzing the two separate motions of the plane. The first motion has the plane fly 170 km at 68° east of north, and the second has it flying 230 km at 48° south of east. By representing these movements as vectors and adding them, we find the direct path the rescue crew should take.

This vector addition can be done graphically or by using trigonometry to break each leg of the plane's journey into its horizontal (east-west) and vertical (north-south) components. After determining the components, we can find the direct distance and bearing from the airport to the plane's location. The past examples and explanations equip us with strategies to calculate the required velocity of the plane relative to the ground and the direction the pilot must head by accounting for the known wind velocities, when necessary.

In summary, to find the direction and distance for the rescue crew, we add the vectors representing the plane's path, utilizing trigonometry to solve the components and then applying vector sum principles to find the result. This procedure allows us to efficiently direct the rescue efforts.

Answer:

Explanation:

We shall write velocities in vector form

Ship A travels in the direction of 32 °west of north with velocity 28 mph

V₁ = - 28 Sin 32 i + 28 Cos 32 j

Ship B travels in the direction of 24 ° east  of north with velocity 35 mph

V₂ = 35 Sin 24 i + 35 Cos 24 j

Their relative velocity

= V₁ -V₂ =  - 28 Sin 32 i + 28 Cos 32 j -  (35 Sin 24 i + 35 Cos 24 j )

-14.83 i - 14.23 i + 23.74 j - 31.97 j

= - 29.06 i - 8.23 j

Distance between them = relative velocity x time

- 29.06 i - 8.23 j x 2

= - 58.12 i - 16.46 j

magnitude²  =( 58.12 ) ² + ( 16.46)² = 60.40²

magnitude = 60.40 km

Speed of ship A as seen by ship B

= Relative velocity of A wrt B

= - 28 Sin 32 i + 28 Cos 32 j -  (35 Sin 24 i + 35 Cos 24 j )

 =  - 29.06 i - 8.23 j

To determine how many yards are in a mile, knowing that a mile equals 5280 feet and a yard contains 3 feet, divide the total feet in a mile by the feet in a yard, resulting in 1760 yards in a mile.

To find how many yards are there in a mile, given that a mile is 5280 feet long and a yard contains 3 feet, we can divide the total number of feet in a mile by the number of feet in a yard. Using the formula for conversion, we calculate:

Yards in a mile = Total feet in a mile ÷ Feet in a yard

By substituting the given values:

Yards in a mile = 5280 ft ÷ 3 ft

Yards in a mile = 1760

This calculation clearly shows that there are 1760 yards in a mile. This example emphasizes the importance of understanding unit conversions in mathematics, allowing us to easily switch between units of measurement.

Answer:

a)Vg=13.42m/s :Speed with which the ball hits the ground

b) t₁= 2.74s : Time the ball remains in the air

c)h=9.19m: Maximum height reached by the ball

Explanation:

We apply the kinematic equations of parabolic motion:

a) Vg= Vo

Vg:speed with which the ball hits the ground

Vo: initial speed

Initial Speed ​​Calculation

[tex]v_{o} =\sqrt{v_{ox}^{2} +v_{oy} ^{2}  }[/tex]

[tex]v_{o} =\sqrt{16^{2} +12^{2}  }[/tex]

Vo=13.42m/s

Vg=13.42m/s

b)Calculation of the time the ball remains in the air

t₁=2*t₂

t₁;time the ball remains in the air

t₂ time when the ball reaches the maximum height

Vf=Vo-g*t₂ : When the ball reaches the maximum height Vf = 0

0=13.42-9.8*t₂

9.8*t₂=13.42

t₂=13.42 ÷9.8

t₂=1.37s

t₁=2*1.37s

t₁= 2.74s

c)Calculation of the maximum height reached by the ball

When the ball reaches the maximum height Vf = 0

Vf²=V₀²-2*g*h

0= V₀²-2*g*h

2*g*h= V₀²

h= V₀² ÷  2*g

h= 13.42² ÷2*9.8

h=9.19m

Answer:

The magnitude of resultant vector and direction are 1.843 m and 77.47° east of north.

Explanation:

Given that,

Magnitude of displacement due to east = 2.8 km

Magnitude of displacement due to north = 2.8 km

Magnitude of displacement due to west = 2.4 km

Magnitude of displacement due to south = 1 km

We need to calculate the resultant of the displacement

[tex]D = d_{1}+d_{2}+d_{3}+d_{4}[/tex]

[tex]D=2.8\hat{i}+2.8\hat{j}-2.4\hat{i}-1\hat{j}[/tex]

[tex]D=0.4\hat{i}+1.8\hat{j}[/tex]

The magnitude of the resultant vector

[tex]D=\sqrt{(0.4)^2+(1.8)^2}[/tex]

[tex]D=1.843\ m[/tex]

We need to calculate the direction

Using formula of direction

[tex]\tan\theta=\dfrac{j}{i}[/tex]

Put the value into the formula

[tex]\tan\theta=\dfrac{1.8}{0.4}[/tex]

[tex]\theta=\tan^{-1}4.5[/tex]

[tex]\theta=77.47^{\circ}[/tex]

Hence, The magnitude of resultant vector and direction are 1.843 m and 77.47° east of north.

Answer:

Explanation:

The car is moving with uniform velocity . Hence there is no acceleration in the car .It indicates that net force on the car is zero . Since force in backward direction is exerted by the wind,  to make net force zero , the forward push by the car must be equal to backward force by the wind. In other words

Forward force by car = backward force by wind = 5000 N.

Answer:

The strength of the field is 22.84 N/C.

Explanation:

Given that,

Speed [tex]v= 7.5\times10^{5}\ m/s[/tex]

Distance = 7.0 cm

We need to calculate the acceleration

Using equation of motion

[tex]v^2-u^2=2as[/tex]

Put the value in the equation

[tex]0-(7.5\times10^{5})^2=2\times a\times7.0\times10^{-2}[/tex]

[tex]a =-\dfrac{(7.5\times10^{5})^2}{2\times7.0\times10^{-2}}[/tex]

[tex]a =-4.017\times10^{12}\ m/s^2[/tex]

We need to calculate the strength of the field

Using newton's second law and electric force

[tex]F = ma = qE[/tex]

[tex]-qE=-ma[/tex]

[tex]E=\dfrac{ma}{q}[/tex]

Put the value into the formula

[tex]E=\dfrac{9.1\times10^{-31}\times4.017\times10^{12}}{1.6\times10^{-19}}[/tex]

[tex]E=22.84\ N/C[/tex]

Hence, The strength of the field is 22.84 N/C.

Final answer:

The strength of the electric field that can stop an electron moving at 7.5 x 10^5 m/s within a distance of 7 cm can be calculated using the work-energy principle, where the work done by the electric field is equal to the change in kinetic energy of the electron.

Explanation:

The strength of the electric field required to bring an electron moving to the right at 7.5 x 105 m/s to rest in a distance of 7.0 cm can be found using the work-energy principle and knowing the force exerted by an electric field on a charge. The work done by the electric field is equal to the change in kinetic energy of the electron, which is initially ½ mv2 and becomes zero when the electron is at rest.

To calculate the strength of the field, we can use:

Work (W) = Electric field (E) x Charge (e) x Distance (d)

½ mv2 = E * e * d

where m is the mass of the electron, v is its initial velocity, e is the elementary charge (approximately 1.6 x 10−12 C), and d is the distance (7.0 cm or 0.07 m). We solve for E to find the strength of the electric field

Answer:

Her velocity at the bottom of the hill is 15.61m/s and she travel up the 30° slope 24.85m

Explanation:

For simplicity purpose, we can analyze the section of the snowboarder's travel in the hill, in the horizontal surface and in the slope separately.

In the hill, we will say that the x-axis is parallel to the hill, and y-axis is perpendicular. Using geometry, we can see that the angle of the snowboarder's weight force from the y-axis is 15°. The velocity of the snowboarder will increase in the direction parallel to the hill, in a constant acceleration motion:

[tex]F_x: W_x = ma\\W*sin(15) = ma\\mg*sin(15) = ma\\a = g*sin(15) = 9.81m/s^2 * sin(15) = 2.54m/s^2[/tex]

With the acceleration, we can use the equations for constant acceleration motion:

[tex]v_f^2 - v_o^2 = 2a*d\\v_f^2 - (0m/s)^2=2*2.54m/s^2*48m\\vf = \sqrt{2*2.54m/s^2*48m}=15.61 m/s[/tex]

This would be her velocity at the bottom of the hill.

As there is no friction, she would reach the bottom of the slope with this velocity.

In the slope, the line of reasoning is similar as in the hill, with the difference that the acceleration will oppose velocity.

[tex]F_x: -W_x = ma\\-W*sin(30) = ma\\-mg*sin(30) = ma\\a = -g*sin(30) = -9.81m/s^2 * sin(30) = -4.905m/s^2[/tex]

[tex]v_f^2-v_o^2=2a*d\\d=\frac{(v_f^2-v_o^2)}{2a}=\frac{((0m/s)^2-(15.61m/s)^2)}{2(-4.905m/s^2)} = 24.85m[/tex]

The speed of the snowboarder at the bottom of the hill is 15.62 m/s.

The distance the snowboarder travel up the 30° slope is 24.9 m.

The acceleration of the snowboarder is calculated as follows;

[tex]W sin\theta - F_f = ma\\\\mgsin\theta - 0 = ma\\\\mg sin(\theta) = ma\\\\a = g(sin\theta)\\\\a = 9.8 \times sin(15)\\\\a = 2.54 \ m/s^2[/tex]

The speed of the snowboarder at the bottom of the hill is calculated as follows;

[tex]v^2 = u^2 + 2ah\\\\v^2 = 0 + 2ah\\\\v = \sqrt{2ah} \\\\v = \sqrt{2(2.54)(48)} \\\\v = 15.62 \ m/s[/tex]

The acceleration of the snowboarder up 30° slope is calculated;

[tex]-Wsin(\theta)- F_f = ma\\\\-Wsin(\theta) -0 = ma\\\\-mgsin(\theta)= ma\\\\-gsin(\theta) = a\\\\a = -9.8 \times sin(30)\\\\a = -4.9 \ m/s^2[/tex]

The distance the snowboarder travel up the 30° slope is calculated as follows;

[tex]v^2 = u^2 - 2ah\\\\-2ah = v^2- u^2\\\\-2ah = v^2 -0\\\\-2ah = v^2\\\\h = \frac{v^2}{-2a} \\\\h = \frac{(15.62)^2}{-2(-4.9)} \\\\h = 24.9 \ m[/tex]

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Answer:

[tex]g'=3.71\ m/s^2[/tex]

Explanation:

Given that,

Time period of a pendulum on the earth's surface, T₁ = 1.2 s

Time period of the same pendulum on Mercury, T₂ = 1.95 s

The time period of the pendulum is given by :

[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

On earth :

[tex]T_1=2\pi \sqrt{\dfrac{l}{g}}[/tex]

[tex]1.2=2\pi \sqrt{\dfrac{l}{9.8}}[/tex].............(1)

Let g' is the acceleration due to gravity on Mercury. So,

[tex]1.95=2\pi \sqrt{\dfrac{l}{g'}}[/tex]............(2)

From equation (1) and (2) :

[tex]\dfrac{1.2}{1.95}=\sqrt{\dfrac{g'}{9.8}}[/tex]

[tex]g'=(\dfrac{1.2}{1.95})^2\times 9.8[/tex]

[tex]g'=3.71\ m/s^2[/tex]

So, the acceleration due to gravity on the mercury is [tex]3.71\ m/s^2[/tex]. Hence, this is the required solution.

Answer:

Electric potential, E = 2100 volts

Explanation:

Given that,

Electric field, E = 3000 N/C

We need to find the electric potential at a point 0.7 m above the surface, d = 0.7 m

The electric potential is given by :

[tex]V=E\times d[/tex]

[tex]V=3000\ N/C\times 0.7\ m[/tex]

V = 2100 volts

So, the electric potential at a point 0.7 m above the surface is 2100 volts. Hence, this is the required solution.

Answer:

[tex]F_{max}=2.95*10^{5}N[/tex]

[tex]\Delta l=0.25cm[/tex]

Explanation:

E=1.50x10^10 N/m2     Young's modulus of bone

σmax=1.50x10^8 N/m2       Max stress tolerated by the bone

Relation between stress and Force:

[tex]\sigma=\frac{F}{A}=\frac{F}{\pi*d^{2}/4}[/tex]

[tex]F_{max}=\sigma_{max}*\pi*d^{2}/4}=1.50*10^{8}*\pi*(2.5*10^{-2})^{2}=2.95*10^{5}N[/tex]

Relation between stress and strain:

Young's modulus is defined by the ratio of longitudinal stress σ , to the longitudinal strain ε:

[tex]E=\frac{\sigma}{\epsilon}[/tex]    

[tex]\epsilon=\frac{\Delta l}{l}[/tex]      

We solve these equations to find the bone compression:

[tex]\Delta l=l*\frac{\sigma}{E}=25*\frac{1.50*10^{8}}{1.50*10^{10}}=0.25cm[/tex]      

Final answer:

To find the maximum force that can be exerted on the femur bone in the leg, we need to calculate the stress using Young's modulus. The maximum force is approximately 7.35 * 10^7 N. To find the amount by which the bone shortens, we need to calculate the strain using Young's modulus and the stress.

Explanation:

To find the maximum force that can be exerted on the femur bone in the leg, we need to calculate the stress. The stress is equal to the force divided by the cross-sectional area of the bone. The cross-sectional area can be determined using the diameter of the bone.

(a) The diameter of the bone is 2.50 cm, which is equal to 0.025 m. The cross-sectional area can be calculated using the formula for the area of a circle: π * (radius)^2. In this case, the radius is half of the diameter, so the area is approximately 0.4909 m2. To find the maximum force, we can use the formula for stress: stress = force / area. Rearranging the formula, we have: force = stress * area. Plugging in the values, we get: force = (1.50 * 108 N/m2) * (0.4909 m2). The maximum force that can be exerted on the femur bone is approximately 7.35 * 107 N.

(b) To find the amount by which the bone shortens, we need to calculate the strain. The strain is equal to the change in length divided by the original length of the bone. The change in length can be determined using the formula for strain: strain = change in length / original length. Rearranging the formula, we have: change in length = strain * original length. We can calculate the strain using the stress and Young's modulus: strain = stress / Young's modulus. Plugging in the values, we get: strain = (1.50 * 108 N/m2) / (1.50 * 1010 N/m2). The change in length can be calculated using the formula: change in length = strain * original length. Plugging in the values, we get: change in length = (1.50 * 108 N/m2) / (1.50 * 1010 N/m2) * 25.0 cm.

Answer:

110.27 m/s or 396.972 km/h

Explanation:

F = Force

m = Mass = 84 kg

g = Acceleration due to gravity = 9.81 m/s²

C = Drag coefficient = 0.7

ρ = Density of air = 1.21 kg/m³

A = Surface area = 0.16 m²

v = Terminal velocity

F = ma

[tex]F=\frac{1}{2}\rho CAv^2\\\Rightarrow ma=\frac{1}{2}\rho CAv^2\\\Rightarrow v=\sqrt{2\frac{ma}{\rho CA}}\\\Rightarrow v=\sqrt{2\frac{84\times 9.81}{1.21\times 0.7\times 0.16}}\\\Rightarrow v=110.27\ m/s[/tex]

Converting to km/h

[tex]\frac{110.27}{1000}\times 3600=396.972\ km/h[/tex]

Terminal velocity of the skydiver is 110.27 m/s or 396.972 km/h

Explanation:

Every rotating body experiences centrifugal force. Due to this force the body tends to bulge out around it mid point and gets flattened at the poles. Same is applicable to Earth as well. Since the Earth is rotating at a very high speed, its equator gets bulged out due to centrifugal force. Because of this bulged equator, Earth's pole to pole diameter and equatorial diameter has difference of around 42.76 km. It is flatter on the poles. This also proves that Earth is not a perfect sphere.

Answer and Explanation:

The reason for the not being perfectly spherical ad bulging out at the equator is that The centripetal force acting toward's the earth gravitational center tries to keep the Earth in perfect spherical shape.

Also the angular momentum of the orbiting planet influences the bulge,

The greater angular momentum results in more bulge while the lower value of it results in lesser bulge and more perfect spherical shape.

Also, a greater amount of force directed towards the center and acting on the object at the equator results in the bulges at the equator whereas at poles this force is not required and hence radius is lower in that region.

Answer:

(a). The speed of the electron is [tex]3.68\times10^{4}\ m/s[/tex]

(b). The distance traveled by the electron is [tex]4.53\times10^{-5}\ m[/tex]

Explanation:

Given that,

Initial velocity = 50 km/s

Electric field  = 50 N/C

Time = 1.5 ns

(a). We need to calculate the speed of the electron 1.5 n s after entering this region

Using newton's second law

[tex]F = ma[/tex].....(I)

Using formula of electric force

[tex]F = qE[/tex].....(II)

from equation (I) and (II)

[tex]-qE= ma[/tex]

[tex]a = \dfrac{-qE}{m}[/tex]

(a). We need to calculate the speed of the electron

Using equation of motion

[tex]v = u+at[/tex]

Put the value of a in the equation of motion

[tex]v = 50\times10^{3}-\dfrac{1.6\times10^{-19}\times50}{9.1\times10^{-31}}\times1.5\times10^{-9}[/tex]

[tex]v=36813.18\ m/s[/tex]

[tex]v =3.68\times10^{4}\ m/s[/tex]

(b). We need to calculate the distance traveled by the electron

Using formula of distance

[tex]s = ut+\dfrac{1}{2}at^2[/tex]

Put the value in the equation

[tex]s = 3.68\times10^{4}\times1.5\times10^{-9}-\dfrac{1}{2}\times\dfrac{1.6\times10^{-19}\times50}{9.1\times10^{-31}}\times(1.5\times10^{-9})^2[/tex]

[tex]s=0.0000453\ m[/tex]

[tex]s=4.53\times10^{-5}\ m[/tex]

Hence, (a). The speed of the electron is [tex]3.68\times10^{4}\ m/s[/tex]

(b). The distance traveled by the electron is [tex]4.53\times10^{-5}\ m[/tex]

Explanation:

The momentum of an object is given by :

[tex]p=m\times v[/tex]............(1)

m is the mas of the object

v is the speed of the object

According to question, arrow's mass is doubled and the speed is halved. So,

m' = 2m

v' = v/2

The new momentum becomes :

[tex]p'=2m\times \dfrac{v}{2}[/tex]

p' = mv

p' = p

So, the momentum remains the same. The momentum is changed by a factor of 1. Hence, this is the required solution.

Answer:

3.06 seconds time passes before the watermelon has the same velocity

watermelon going at speed 59.9 m/s

watermelon traveling when it hits the ground at speed is 79.19 m/s

Explanation:

given data

height = 320 m

speed = 30 m/s

to find out

How much time passes before the watermelon has the same velocity and How fast is the watermelon going and How fast is the watermelon traveling

solution

we will use here equation of motion that is

v = u + at    ....................1

here v is velocity 30 m/s and u is initial speed i.e zero and a is acceleration i.e 9.8 m/s²

put the value and find time t

30 = 0 + 9.8 (t)

t = 3.06 s

so 3.06 seconds time passes before the watermelon has the same velocity

and

we know superman cover distance is = velocity × time

so distance = 30 × t

and distance formula for watermelon is

distance = ut + 0.5×a×t²    .............2

here u is initial speed i.e 0 and a is acceleration i.e 9.8 m/s² and h is 30 × t

30 × t = 0 + 0.5×9.8×t²

t = 6.12 s

so  by equation 1

v = u + at

v = 0 + 9.8 ( 6.12)

v = 59.9 m/s

so watermelon going at speed 59.9 m/s

and

watermelon traveling speed formula is by equation of motion

v² - u² = 2as      ......................3

here v is speed and u is initial speed i.e 0 and a is acceleration i.e 9.8 m/s² and s is distance i.e 320 m

v² - 0 = 2(9.8) 320

v = 79.19 m/s

so watermelon traveling when it hits the ground at speed is 79.19 m/s

Answer:

x=4.06m

Explanation:

A body that moves with constant acceleration means that it moves in "a uniformly accelerated movement", which means that if the velocity is plotted with respect to time we will find a line and its slope will be the value of the acceleration, it determines how much it changes the speed with respect to time.

When performing a mathematical demonstration, it is found that the equations that define this movement are as follows.

Vf=Vo+a.t  (1)\\\\

{Vf^{2}-Vo^2}/{2.a} =X(2)\\\\

X=Xo+ VoT+0.5at^{2}    (3)\\

Where

Vf = final speed

Vo = Initial speed

T = time

A = acceleration

X = displacement

In conclusion to solve any problem related to a body that moves with constant acceleration we use the 3 above equations and use algebra to solve

for this problem

Vf=7.6m/s

t=1.07

Vo=0

we can use the ecuation number one to find the acceleration

a=(Vf-Vo)/t

a=(7.6-0)/1.07=7.1m/s^2

then we can use the ecuation number 2 to find the distance

{Vf^{2}-Vo^2}/{2.a} =X

(7.6^2-0^2)/(2x7.1)=4.06m

To get a sharp image of the Sun, the paper should be placed at the focal length of the lens, which is 10 centimeters away from the lens. The image is in focus at this point because the light rays from the Sun are effectively parallel when they reach the lens, which then focuses these rays at its focal point.

Given the sun is so far away, the light it emits is nearly parallel by the time it reaches Earth. When using a lens to cast an image of the Sun, the point where the image is in focus, that is, the focal point, is also the focal length of the lens.

In this case, the student uses a lens with f = 10 cm, meaning the focal length of the lens is 10 centimeters. To get a sharp image, the paper on which the image is being projected should be placed 10 cm away from the lens, or at the focal length of the lens. This is because the light is in sharp focus at this distance, creating a clear image on the paper.

An important concept here is that the Sun is an astronomical unit away, so the light rays from the Sun are essentially parallel when they reach the lens. The lens then focuses these parallel rays to its focal point, forming a sharp image at a distance equal to its focal length.

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Answer:

The magnitude of the electric field is 129375 N/C toward south.

Explanation:

Given that,

Electric force [tex]F=2.07\times10^{-14}\ N[/tex]

(A). We need to calculate the magnitude of the electric field

Using formula of electric field

[tex]F = qE[/tex]

[tex]E=\dfrac{F}{q}[/tex]

Where, q = charge of proton

E = electric field

[tex]E=\dfrac{2.07\times10^{-14}}{1.6\times10^{-19}}[/tex]

[tex]E=129375\ N/C[/tex]

(B). The direction of the electric field is toward the direction of the force.

So, The direction of the electric field is toward south

Hence, The magnitude of the electric field is 129375 N/C toward south.

Answer:

electric flux is 280  Nm²/C  

so correct option is D 280  Nm²/C

Explanation:

radius r = 0.50 m

angle = 30 degree

field strength = 713 N/C

to find out

the electric flux through the surface

solution

we find here electric flux by given formula that is

electric flux = field strength × area× cos∅   .......1

here area = πr² = π(0.50)²

put here all value in equation  1

electric flux = field strength × area× cos∅  

electric flux = 713 × π(0.50)² × cos60

we consider the cosine of the angle between the direction of the field and the normal to the surface of the disk

so we use cos60

electric flux = 280  Nm²/C

so correct option is D 280  Nm²/C

Answer:

total distance = 1868.478 m

Explanation:

given data

accelerate = 1.68 m/s²

time = 14.2 s

constant time = 68 s

speed = 3.70 m/s²

to find out

total distance

solution

we know train start at rest so final velocity will be after 14 .2 s is

velocity final = acceleration × time      ..............1

final velocity = 1.68 × 14.2

final velocity = 23.856 m/s²

and for stop train we need time that is

final velocity = u + at

23.856 = 0 + 3.70(t)

t = 6.44 s

and

distance = ut + 1/2 × at²     ...........2

here u is initial velocity and t is time for 14.2 sec

distance 1 = 0 + 1/2 × 1.68 (14.2)²

distance 1 = 169.37 m

and

distance for 68 sec

distance 2= final velocity × time

distance 2= 23.856 × 68

distance 2 = 1622.208 m

and

distance for 6.44 sec

distance 3 = ut + 1/2 × at²

distance 3 = 23.856(6.44) - 0.5 (3.70) (6.44)²

distance 3 = 76.90 m

so

total distance = distance 1 + distance 2 + distance 3

total distance = 169.37 + 1622.208 + 76.90

total distance = 1868.478 m

Answer:

1868.5 m

Explanation:

For AB :

u = 0 m/s

a = + 1.68 m/s^2

t = 14.2 s

Let the distance is s1 and the velocity at B is v.

Use first equation of motion

v = u + at

v = 0 + 1.68 x 14.2 = 23.856 m/s

Use third equation of motion

[tex]v^{2}=u^{2}+2as_{1}[/tex]

[tex]23.856^{2}=0^{2}+2\times1.68\times s_{1}[/tex]

s1 = 169.38 m

For BC:

Let the distance is s2.

s2 = v x t

s2 = 23.856 x 68 = 1622.21 m

For CD:

u = 23.856 m/s

a = - 3.7 m/s^2

v = 0

Let the distance is s3.

Use third equation of motion

[tex]v^{2}=u^{2}+2as_{3}[/tex]

[tex]0^{2}=23.856^{2}-2\times 3.7 \times s_{3}[/tex]

s3 = 76.91 m

The total distance traveled is

s = s1 + s2 + s3

s = 169.38 + 1622.21 + 76.91 = 1868.5 m

Thus, the total distance traveled is 1868.5 m.  

Answer:

[tex]q=+8.34*10^{-7}C}[/tex]

Explanation:

The potential V due to a charge q,  at a distance r, is:

[tex]V=k\frac{q}{r}[/tex]

k=8.99×109 N·m^2/C^2      :Coulomb constant

We replace the values in order to find q:

[tex]q=\frac{V*r}{k}=\frac{500*15}{8.99*10^{9}}=8.34*10^{-7}C[/tex]

Answer:

i apolagize im late but yeah bois 700 points

Explanation:

Answer:

Its initial velocity will be greater than final velocity so option (b) will be correct option  

Explanation:

As we throw the any object vertically the motion of the object will be opposes by the gravity.

And as the velocity of object is opposes by gravity, the final velocity goes on decreasing and finally it becomes zero.

So the initial velocity is always greater than final velocity when the object is thrown vertically upward.

So option (b) will be the correct option  

Answer:

The answer is very close to [tex]N_e=2.989\times10^{26}[/tex], where [tex]N_e[/tex] is the number of electrons.

Explanation:

First we take into account that the block weighs 1Kg, and that the number of protons and electrons is the same. As the electron mass is tiny even compared to that of the proton and neutrons we can neglect it in our considerations.

Let's start by equating the mass of all protons and neutrons to the mass of the  of the object:

[tex]N_p m_p+N_n m_n=1[/tex]

Where [tex]N_p[/tex] and [tex]N_n[/tex] is the number of protons and neutrons respectively. [tex]m_p[/tex] and [tex]m_n[/tex] is the mass of an proton and a neutron respectively. Because the number of protons and neutrons is equal we can say the following [tex]N_p=N_n=N[/tex], thus we have:

[tex]N_p m_p+N_n m_n=N(m_e+m_p)=1Kg \implies N=\frac{1}{m_p+m_n} [/tex]

On the other hand we have that the sum of all charges is less than the absolute value of 1C, we can express this by the following:

[tex]-1<N_p\cdot e-N_e\cdot e<1[/tex]

[tex]\implies -1<N\cdot e-N_e\cdot e<1[/tex]

Where [tex]e[/tex] is the proton charge (same as for the electron). We continue with the inequality:

[tex]-N\cdot e-1<N_p\cdot e-N_e\cdot e<-N\cdot e+1[/tex]

[tex]\implies \frac{N\cdot e+1}{e}>N_e>\frac{N\cdot e-1}{e}[/tex]

[tex]\implies \frac{(m_e+m_p)^{-1}\cdot e+1}{e}>N_e>\frac{(m_e+m_p)^{-1}\cdot e-1}{e}[/tex]

We have the estimated number of electrons bound. Because

[tex](m_e+m_p)^{-1}\cdot e>>1[/tex] We can neglect the ones on the rightmost and leftmost parts of the inequality. We then have

[tex]N_e\approx\frac{(m_p+m_n)^{-1}\cdot e}{e}[/tex]

Using the table values of the mass of the proton, mass of the neutron and the electron charge e we get

[tex]N_e\approx\frac{(1.672\times 10^{-27}+1.674\times 10^{-27})^{-1}\cdot e}{e}=(1.672\times 10^{-27}+1.674\times 10^{-27})^{-1}[/tex]

[tex]\, =2.989\times 10^{26}[/tex] electrons

Answer:

The wave equation is [tex]\frac{d^{2}u }{dt^{2} }[/tex] = [tex]c^{2}[/tex] [tex]\frac{d^{2}u }{dx^{2} }[/tex]

a sinusoidal wave can be u = Acos( ax + bt) + B*sin(ax + bt)

where A, a, B and b are real constants. (here you also can add a phase to the arguments of the sin and cosine)

then [tex]\frac{d^{2}u }{dt^{2} }[/tex] = [tex]b^{2}[/tex]*( -Acos(ax + bt) - B*sin(ax + bt))

and [tex]c^{2}[/tex] [tex]\frac{d^{2}u }{dx^{2} }[/tex]= [tex]ac^{2}[/tex]*( -Acos(ax + bt) - B*sin(ax + bt))

then if a*c = b, this is a solution of the wave equation.

Answer:

a) [tex]F_a=0.152 \mu N[/tex]

b) [tex]F_b=203.182 \mu N[/tex]

Explanation:

The center of mass of an homogeneous sphere is its center, therefore you can use Newton's universal law of gravitation to find both questions.

[tex]F_g=G\frac{m_1m_2}{d}[/tex]

[tex]G=6.674*10^{-11} NmKg^{-2}[/tex]

a) d = 19m

[tex]F_a = G\frac{8.4*10^{4}*9.8}{19^2}[/tex]

[tex]F_a=0.152 \mu N[/tex]

b) d = 0.52

[tex]F_b = G\frac{8.4*10^{4}*9.8}{0.52^2}[/tex]

[tex]F_b=203.182 \mu N[/tex]

Answer:

(a) GF = 1.522 x (10 ^ -7)  N

(b) GF = 2.032 x (10 ^ -4)  N

Explanation:

The magnitude of the gravitational force follows this equation :

GF = (G x m1 x m2) / (d ^ 2)

Where G is the gravitational constant universal.

G = 6.674 x (10 ^ -11).{[N.(m^ 2)] / (Kg ^ 2)}

m1 is the mass from the first body

m2 is the mass from the second body

And d is the distance between each center of mass

m2 is a particle so m2 it is a center of mass itself

The center of mass from the sphere is in it center because the sphere has uniform density

For (a) d = 19 m

GF = {6.674 x (10 ^ -11).{[N.(m ^ 2)] / (Kg ^ 2)} x 8.4 x (10 ^ 4) Kg x 9.8 Kg} / [(19 m)^ 2]

GF = 1.522 x (10 ^ -7)  N

For (b) d = 0.52 m

GF = 2.032 x (10 ^ -4)  N

Notice that we have got all the data in congruent units

Also notice that the force in (b) is bigger than the force in (a) because the distance is shorter

Answer:

Explanation:

Energy stored in a capacitor

= 1/2 CV²

C is capacitance and V is potential of the capacitor .

When capacitor is charged to 24 V ,

E₁ = 1/2 x 2.4 x 24 x24 = 691.2 J

When it is charged to 12 volt

E₂ = 1/2 CV²

.5 X 2.4 X 12 X12

= 172.8 J