A gray kangaroo can bound across level ground with each jump carrying it 9.6 m from the takeoff point. Typically the kangaroo leaves the ground at a 28º angle. If this is so: Part A) What is its takeoff speed? Express your answer to two significant figures and include the appropriate units. Part B) What is its maximum height above the ground? Express your answer to two significant figures and include the appropriate units

Answer:

23 cm

Explanation:

m = 64.3 kg, diameter = 0.910 cm

radius, r = 0.455 cm = 4.55 x 10^-3 m

A = 3.14 x (4.55 x 10^-3)^2 = 6.5 x 10^-5 m^2

L = 32.2 m

Y = 1.35 x 10^9 Pa

Let the stretched length is l.

Use the formula for Young's modulus

Y = mg L / A l

l = m g L / A Y

l = (64.3 x 9.8 x 32.2) / (6.5 x 10^-5 x 1.35 x 10^9)

l = 0.23 m

l = 23 cm

Answer:

y = 43.2 cm

Explanation:

As we know by the formula of diffraction we have

[tex]a sin\theta = N\lambda[/tex]

here we have

[tex]\theta = 17.4[/tex]

N = 4

[tex]\lambda = 602 nm[/tex]

now we have

[tex]a sin(17.4) = 4(602\times 10^{-9})[/tex]

[tex]a = 8.05 \times 10^{-6} m[/tex]

now the distance of screen is 138 cm

now we can say

[tex]\frac{y}{L} = tan\theta[/tex]

[tex]y = L tan(\theta)[/tex]

[tex]y = 138 tan(17.4) = 43.2 cm[/tex]

Answer:

Part a)

[tex]Q = 2.47 \times 10^6[/tex]

Part b)

t = 4950.3 s

Explanation:

As we know that heat required to raise the temperature of container and water in it is given as

[tex]Q = m_1s_2\Delta T_1 + m_2s_2\Delta T_2[/tex]

here we know that

[tex]m_1 = 0.750[/tex]

[tex]s_1 = 900[/tex]

[tex]m_2 = 2.50 kg[/tex]

[tex]s_2 = 4186[/tex]

[tex]\Delta T_1 = \Delta T_2 = 100 - 30 = 70^oC[/tex]

now we have

[tex]Q_1 = 0.750(900)(70) + (2.5)(4186)(70) = 779800 J[/tex]

now heat require to boil the water

[tex]Q = mL[/tex]

here

m = 0.750 kg

[tex]L = 2.25 \times 10^6 J/kg[/tex]

now we have

[tex]Q_2 = 0.750(2.25 \times 10^6) = 1.7 \times 10^6 J[/tex]

Now total heat required is given as

[tex]Q = Q_1 + Q_2[/tex]

[tex]Q = 779800 + 1.7 \times 10^6 = 2.47 \times 10^6 J[/tex]

Part b)

Time taken to heat the water is given as

[tex]t = \frac{Q}{P}[/tex]

here we know that

power = 500 W

now we have

[tex]t = \frac{2.47 \times 10^6}{500} = 4950.3 s[/tex]

Answer:

Rate of heat is 45.1 kJ/min

Explanation:

Heat required to evaporate the water is given by

Q = mL

here we know that

[tex]L = 2.25 \times 10^6 J/kg[/tex]

now we have

[tex]Q = (0.200)(2.25 \times 10^6 J/kg)[/tex]

[tex]Q = 452.1 kJ[/tex]

now the power is defined as rate of energy

[tex]P = \frac{Q}{t}[/tex]

[tex]P = \frac{452.1 kJ}{10}[/tex]

[tex]P = 45.1 kJ/min[/tex]

Answer:

[tex]6.35\cdot 10^{-9} W[/tex]

Explanation:

The relationship between power and intensity of a sound is given by:

[tex]I=\frac{P}{A}[/tex]

where

I is the intensity

P is the power

A is the area considered

In this problem, we know

[tex]A=2.90\cdot 10^{-3}m^2[/tex] is the surface area of the ear

[tex]I = 2.19\cdot 10^{-6} W/m^2[/tex] is the intensity of the sound

Re-arranging the equation, we can find the power intercepted by the ear:

[tex]P=IA=(2.19\cdot 10^{-6} W/m^2)(2.90\cdot 10^{-3} m^2)=6.35\cdot 10^{-9} W[/tex]

Answer:

anterior

anterior

Explanation:

In the given question is asked that

If a person is standing erect and flexes the trunk on the hip, the center of mass will move ___________ and the line of gravity moves___________ within the base of support.

The current answer to the blanks will be

anterior

anterior

hope this helps any further query can be asked in comment section.

Answer:

A) 854.46 kPa

Explanation:

P₁ = initial pressure of the gas = 400 kPa

P₂ = final pressure of the gas = ?

T₁ = initial temperature of the gas = 110 K

T₂ = final temperature of the gas = 235 K

Using the equation

[tex]\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}[/tex]

Inserting the values

[tex]\frac{400}{110}=\frac{P_{2}}{235}[/tex]

P₂ = 854.46 kPa

Answer:

C

Explanation:

Givens

m = 2 kg

F = 2 * 9.81

F =  19.62 N

x = 0.15 m

Formula

F = k*x

Solution

19.62 = k*0.15

k = 19.62/0.15

k = 130.8 which rounded to the nearest given answer is C

Answer:

Part a)

P = 8.23 kg m/s

Part b)

v = 3.05 m/s

Explanation:

Part a)

momentum of cart 1 is given as

[tex]P_1 = m_1v_1[/tex]

[tex]P_1 = (2.7)(3.7) = 9.99 kg m/s[/tex]

Momentum of cart 2 is given as

[tex]P_2 = m_2v_2[/tex]

[tex]P_2 = (1.1)(-1.6) = -1.76 kg m/s[/tex]

Now total momentum of both carts is given as

[tex]P = P_1 + P_2[/tex]

[tex]P = 8.23 kg m/s[/tex]

Part b)

Since two carts are moving towards each other due to mutual attraction force and there is no external force on two carts so here momentum is always conserved

so here we will have

[tex]P_i = P_f[/tex]

[tex](2.7 kg)v = 8.23[/tex]

[tex]v = 3.05 m/s[/tex]

Answer:

Acceleration of gravity on Noveria = 4.4 m/s²

Explanation:

Commander Shepard, an N7 spectre for Earth, weighs 799 N on the Earth's surface.

We have weight, W = mg

Acceleration due to gravity, g = 9.81m/s²    

799 = m x 9.81

Mass of Shepard, m = 81.45 kg            

She lands on Noveria, a distant planet in our galaxy, she weighs 356 N.

We have weight, W = mg'

                 356 = 81.45 xg'

Acceleration of gravity on Noveria, g' = 4.4 m/s²

Answer:

(a) 6.22 x 10^-6 C

(b) 3.8 x 10^13

Explanation:

Let the second charge is q2 = q

q1 = 1.6 x 10^-19 C

F = 3.5 x 10^9 N

d = 1.6 mm = 1.6 x 10^-3 m

(a) Use the formula of Coulomb's law

F = K q1 x q2 / d^2

3.5 x 10^-9 = 9 x 10^9 x 1.6 x 10^-19 x q / (1.6 x 10^-3)^2

q = 6.22 x 10^-6 C

(b)

Let the number of electrons be n

n = total charge / charge of one electron

n = 6.22 x 10^-6 / (1.6 x 10^-19) = 3.8 x 10^13

From conservation of linear momentum, the magnitude of the velocity of the wreckage after collision is 15.6 m/s while its direction is 53 degrees.

There are four types of collision

In elastic collision, both momentum and energy are conserved. While in inelastic collision, only momentum is conserved.

From the given question, the following parameters are given.

Since the collision is inelastic, they will both move with a common velocity after collision.

Horizontal component

[tex]m_{1}[/tex][tex]v_{1}[/tex] = ([tex]m_{1}[/tex] + [tex]m_{2}[/tex] ) V

1500 x 25 = (1500 + 2500) V

37500 = 4000V

V = 37500 / 4000

V = 9.375 m/s

Vertical component

[tex]m_{2}[/tex][tex]v_{2}[/tex] = ([tex]m_{1}[/tex] + [tex]m_{2}[/tex])V

2500 x 20 = (1500 + 2500)V

50000 = 4000V

V = 50000 / 4000

V = 12.5 m/s

The net velocity will be the magnitude of the velocity of the wreckage after collision

V = [tex]\sqrt{9.4^{2} + 12.5^{2} }[/tex]

V = [tex]\sqrt{244.61}[/tex]

V = 15.6 m/s

The direction will be

Tan Ф = 12.5 / 9.4

Ф = [tex]Tan^{-1}[/tex](1.329)

Ф = 53 degrees.

Therefore,  the magnitude of the velocity of the wreckage after collision is 15.6 m/s while its direction is 53 degrees.

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The velocity of the wreckage after the collision is 32.015 m/s in the direction 38.66° north of east.

This problem is related to the conservation of linear momentum which states the total momentum of an isolated system remains constant if no external forces act on it. Momentum is a vector quantity having both magnitude and direction. The total initial and final momentum in both horizontal (x) and vertical (y) directions must be equal.

Initial momentum of the car is (1500 kg)*(25.0 m/s) = 37500 kg*m/s in the east direction whereas initial momentum of the van is (2500 kg)*(20.0 m/s) = 50000 kg*m/s in the north direction.

Since the collision is perfectly inelastic, the two vehicles stick together after the collision and move as one. Therefore, the final momentum is the vector sum of the individual momenta. We therefore calculate the magnitude of the resultant velocity using Pythagoras theorem, √[(25.0 m/s)² + (20.0 m/s)²] = 32.015 m/s.

To find the direction of the final velocity, we use the tangent of the angle which is equal to the vertical component divided by the horizontal component, which gives us an angle of 38.66° north of east.

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Explanation:

0.05

momentum =Mv

then,

Mv=mv

v2=0.12*6/14

v2=0.05kgm/s

The change in the magnitude of the momentum of the ball is 2.4 kg·m/s.

To calculate the change in the magnitude of the momentum of the ball, we need to find the initial momentum and the final momentum of the ball. Momentum is calculated by multiplying the mass of an object by its velocity. Let's start by calculating the initial momentum:

Initial momentum = mass × initial velocity

Final momentum = mass × final velocity

Change in momentum = final momentum - initial momentum

Plugging in the given values:

Initial momentum = 0.12 kg × 6 m/s

Final momentum = 0.12 kg × (-14 m/s) (since the ball changes direction)

Change in momentum = (-1.68 kg·m/s) - (0.72 kg·m/s) = -2.4 kg·m/s.

The change in the magnitude of the momentum of the ball is 2.4 kg·m/s. However, since the question is asking for the magnitude, we take the absolute value of the change in momentum, which is 2.4 kg·m/s.

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Answer:

314 Joule

Explanation:

m = 10 kg, g = 10 m/s^2, d = 1 m, angle turn = 180 degree = π radian

work = torque x angle turn

torque = force x perpendicular distance

torque = m x g x d = 10 x 10 x 1 = 100 Nm

work = 100 x π

work = 100 x 3.14 = 314 Joule

Final answer:

The work done by a constant torque on a rigid body rotating through an angle of 180° can be found by multiplying the torque by the angle. The torque can be calculated using the equation τ = Iα, where I is the moment of inertia and α is the angular acceleration. Substituting the given values, we find that the work done by the torque on the rigid body is 18000 kg·m^2·rad/s^2.

Explanation:

The work done by a torque on a rigid body is given by the formula W = τθ, where τ is the torque and θ is the angle through which the body rotates. In this case, the torque is constant in both magnitude and direction, so we can use W = τθ. Given that the torque is constant and the body turns through an angle of 180°, we can calculate the work done as follows:

Since τ is constant, we can write W = τθ = τ (180° - 0°). The work done by the torque is equal to the torque multiplied by the change in angle. Substitute the given values into the formula: W = (τ) (180° - 0°) = (τ) (180°). The work done by the torque is equal to the torque multiplied by 180°.

To find the value of the torque, we need to use the equation τ = Iα, where I is the moment of inertia and α is the angular acceleration. In this case, the rigid body has a mass of 10 kg and a distance of 1 m from the pivot. The moment of inertia for a point mass rotating about a fixed axis is given by I = m(r^2), where m is the mass and r is the perpendicular distance from the axis. Substitute the given values into the formula: I = (10 kg)((1 m)^2) = 10 kg·m^2. Since α = a/r and the acceleration due to gravity is 10 m/s^2, we have α = (10 m/s^2)/(1 m) = 10 rad/s^2.

Substitute the values of τ and α into the equation τ = Iα: τ = (10 kg·m^2)(10 rad/s^2) = 100 kg·m^2·rad/s^2. Therefore, the torque is 100 kg·m^2·rad/s^2.

Finally, substitute the values of τ and θ into the equation W = τθ: W = (100 kg·m^2·rad/s^2 )(180°) = 18000 kg·m^2·rad/s^2.

The magnetic force on a wire carrying current towards the south under a magnetic field directed vertically upwards will point towards the East. In order to determine this, use the right-hand rule.

The direction of the magnetic force on a current-carrying wire under a magnetic field can be deduced using the right-hand rule. In this case, with the current flowing towards the south and the magnetic field directed vertically upward, you would point your right thumb in the direction of the current (southwards) and curl your fingers in the direction of the magnetic field (upwards). The palm of your hand will then face toward the direction of the force. In this case, the force would be pointing toward the East.

The right-hand rule is a vital principle in the study of electromagnetism as it aids in identifying the direction of various quantities in magnetic fields.  The magnetic force on a current-carrying wire represents the phenomenon underlying the working of many electric motors.

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Answer:

275.4 kg

Explanation:

specific gravity = 0.918

Density = 0.918 g/cm^3 = 918 kg/m^3

Volume = 100 gallons = 300 litres = 300 x 10^-3 m^3 = 0.3 m^3

Mass = volume x density = 0.3 x 918 = 275.4 kg

Answer:

Part a)

the two frequencies are in ratio of odd numbers so it must be closed at one end

Part b)

L = 34.3 cm

Explanation:

Part a)

Since the shortest frequency is known as fundamental frequency

It is given as

[tex]f_o = 250 Hz[/tex]

next higher frequency is given as

[tex]f_1 = 750 Hz[/tex]

since the two frequencies here are in ratio of

[tex]\frac{f_1}{f_o} = \frac{750}{250} = 3 : 1[/tex]

since the two frequencies are in ratio of odd numbers so it must be closed at one end

Part b)

For the length of the pipe we can say that fundamental frequency is given as

[tex]f_o = \frac{v}{4L}[/tex]

here we have

[tex]250 = \frac{343}{4(L)}[/tex]

now we will have

[tex]L = \frac{343}{4\times 250}[/tex]

[tex]L = 34.3 cm[/tex]

Answer:

[tex]\omega _{f}=0.3107rad/sec[/tex]

partb) [tex]\omega _{f}=14.93rad/sec[/tex]

Explanation:

Since the system is isolated it's angular momentum shall be conserved

[tex]L_{system}=I_{system}\omega \\\\I_{system}=I_{rod}+2\times m\times r^{2}\\\\I_{system}=\frac{1}{12}ml^{2}+2\times 0.2\times (4.8\times 10^{-2})^{2}\\\\I_{system}=1.22845\times 10^{-3}kgm^{2}\\\\L_{system}=1.22845\times 10^{-3}kgm^{2}\times 3.66rad/sec[/tex]

[tex]\L_{system}=4.496\times 10^{-3}kgm^{2}[/tex]

Now the final angular momentum of the system

[tex]L_{fianl}=I_{final}\omega \\\\I_{final}=I_{rod}+2\times m\times r_{f}^{2}\\\\I_{final}=\frac{1}{12}ml^{2}+2\times 0.2\times (0.19)^{2}\\\\I_{final}=0.01447kgm^{2}\\\\L_{final}=0.01447kgm^{2}\times \omega _{final}rad/sec[/tex]

Thus equating initial and final angular momentum we solve for final angular velocity of rod as

[tex]\omega _{f}=\frac{4.496\times 10^{-3}}{0.01447}\\\\\omega _{f}=0.3107rad/sec[/tex]

part b)

When the rings leave the system we again conserve the angular momentum just before the rings leave the system and the instant when they just leave

[tex]\therefore 0.01447=\frac{1}{12}ml^{2}w\\\\\therefore w=\frac{4.582\times 10^{-3}}{3.068\times10^{-4} }\\\\w_{final}=14.93rad/sec[/tex]

Answer:

A)[tex]\omega_{f}=2.92\frac{rev}{min}[/tex].

B)[tex]\omega_{f}=140\frac{rev}{min}[/tex].

Explanation:

A)

For this problem, we will use the conservation of angular momentum.

[tex]L_{0}=L_{f}\\[/tex].

In the beginning, we have that

[tex]L_{0}=I_{0}\omega_{0}\\[/tex]

where [tex]I_{0}[/tex] is the inertia moment of all the system at the starting position, this is the inertia moment of the rod plus the inertia moment of each ring ([tex]mr^{2}[/tex], with [tex]r[/tex] the distance from the ring to the fixed axis and, [tex]m[/tex] its mass) at the starting position and, [tex]\omega_{0}[/tex] is the initial angular velocity. So

[tex]L_{0}=(\frac{1}{12}Ml^{2}+2mr_{0}^{2})\omega_{0}[/tex].

When the rings are at the ends of the rod the angular momentum becomes

[tex]L_{f}=(\frac{1}{12}Ml^{2}+2mr_{f}^{2})\omega_{f}[/tex],

where [tex]r_{f}[/tex] is the distance from the fixed axis to the end of the rod (the final position of the rings).

Using conservation of angular momentum we get

[tex](\frac{1}{12}Ml^{2}+2mr_{0}^{2})\omega_{0}=(\frac{1}{12}Ml^{2}+2mr_{f}^{2})\omega_{f}[/tex].

thus

[tex]\omega_{f}=\frac{(\frac{1}{12}Ml^{2}+2mr_{0}^{2})\omega_{0}}{(\frac{1}{12}Ml^{2}+2mr_{f}^{2})}[/tex]

computing this last expresion we get

[tex]\omega_{f}=\frac{(\frac{1}{12}(2.55*10^{-2})(0.380)^{2}+2(0.200)(4.80*10^{-2})^{2})(35.0)}{(\frac{1}{12}(2.55*10^{-2})(0.380)^2+2(0.200)(0.19)^{2})}[/tex]

[tex]\omega_{f}=2.92\frac{rev}{min}[/tex].

B)

Again we use the conservation of angular momentum. The initial angular momentum if the same as before. The final angular momentum will be

[tex]L_{f}=(\frac{1}{12}Ml^{2})\omega_{f}[/tex],

this time we will not take into account the inertia moment of the rings because they are no longer part of the system (they leave the rod).

[tex](\frac{1}{12}Ml^{2}+2mr_{0}^{2})\omega_{0}=(\frac{1}{12}Ml^{2})\omega_{f}[/tex].

thus

[tex]\omega_{f}=\frac{(\frac{1}{12}Ml^{2}+2mr_{0}^{2})\omega_{0}}{(\frac{1}{12}Ml^{2})}[/tex]

computing this last expresion we get

[tex]\omega_{f}=\frac{(\frac{1}{12}(2.55*10^{-2})(0.380)^{2}+2(0.200)(4.80*10^{-2})^{2})(35.0)}{(\frac{1}{12}(2.55*10^{-2})(0.380)^2})[/tex]

[tex]\omega_{f}=140\frac{rev}{min}[/tex].

Answer:

explained

Explanation:

When the intensity of light is increased on a piece of metal only the number of electron ejected will increase because all other things independent of intensity of light.

Light below certain frequency will not cause any electron emission no matter how intense.

The intensity produces more electron but does not change the maximum kinetic energy of electrons.

Work function is independent of the intensity of light, because it is an intrinsic property of a material.

Answer:

a)

365.3 N/C

b)

3.85 x 10⁴ m/s

Explanation:

q = magnitude of charge on proton = 1.6 x 10⁻¹⁹ C

m = mass of the proton = 1.67 x 10⁻²⁷ kg

d = distance between the plates = 2.10 cm = 0.021 m

t = time interval = 1.10 x 10⁻⁶ sec

E = magnitude of electric field

v₀ = initial velocity = 0 m/s

a = acceleration of the proton

Using the equation

d = v₀ t + (0.5) a t²

0.021 = (0) (1.10 x 10⁻⁶) + (0.5) a (1.10 x 10⁻⁶)²

a = 3.5 x 10¹⁰ m/s²

acceleration of the proton inside electric field is given as

[tex]a =\frac{qE}{m}[/tex]

[tex]3.5\times 10^{10} =\frac{(1.6\times 10^{-19})E}{1.67\times 10^{-27}}[/tex]

E = 365.3 N/C

b)

v = final speed of the proton

using the equation

v = v₀ + a t

v = 0 + (3.5 x 10¹⁰) (1.10 x 10⁻⁶)

v = 3.85 x 10⁴ m/s

Answer:

[tex]v = \sqrt{v_0^2 - \frac{2k}{3}(s^3 - s_0^3)}[/tex]

v = 9.67 m/s

Explanation:

As we know that acceleration is rate of change in velocity

so it is defined as

[tex]a = \frac{dv}{dt}[/tex]

[tex]a = v\frac{dv}{ds}[/tex]

here we know that

[tex]a = - ks^2 = v\frac{dv}{ds}[/tex]

now we have

[tex]vdv = - ks^2ds[/tex]

integrate both sides we have

[tex]\int vdv = -k \int s^2ds[/tex]

[tex]\frac{v^2}{2} - \frac{v_0^2}{2} = -k(\frac{s^3}{3} - \frac{s_0^3}{3})[/tex]

[tex]v^2 = v_0^2 - \frac{2k}{3}(s^3 - s_0^3)[/tex]

here we know that

[tex]v_0 = 10 m/s[/tex]

[tex]s_0 = 3 m[/tex]

[tex]v^2 = 10^2 - \frac{2(0.10)}{3}(5^3 - 3^3)[/tex]

[tex]v = 9.67 m/s[/tex]

Answer:

a) 7250.5 N

b) 4.6 m/s²

Explanation:

a)

F = applied force = 8000 N

θ = angle with the horizontal = 65 deg

Consider the motion along the vertical direction :

[tex]F_{y}[/tex] = Applied force in vertical direction in upward direction = F Sinθ = 8000 Sin65 = 7250.5 N

[tex]F_{g}[/tex] = weight of the plane in vertical direction in downward direction = ?

[tex]a_{y}[/tex] = Acceleration in vertical direction = 0 m/s²

Taking the force in upward direction as positive and in downward direction as negative, the force equation along the vertical direction can be written as

[tex]F_{y}-F_{g} = m a_{y}[/tex]

[tex]7250.5 -F_{g} = m (0)[/tex]

[tex]F_{g}[/tex] = 7250.5 N

b)

m = mass of the plane

force of gravity is given as

[tex]F_{g} = mg [/tex]

[tex]7250.5 = m(9.8) [/tex]

m = 739.85 kg

Consider the motion along the horizontal direction

[tex]F_{x}[/tex] = Applied force in horizontal direction = F Cosθ = 8000 Cos65 = 3381 N

[tex]a_{x}[/tex] = Acceleration in horizontal direction

Acceleration in horizontal direction is given as

[tex]a_{x}=\frac{F_{x}}{m}[/tex]

[tex]a_{x}=\frac{3381}{739.85}[/tex]

[tex]a_{x}[/tex] = 4.6 m/s²

Answer:It is rising at a rate of [tex]7.5cm/min[/tex]

Explanation:

We have volume of trapezoid equals

[tex]V=Area\times Length\\\\V=\frac{1}{2}(a+b)h\times L[/tex]

Thus at any time 't' we have

[tex]V(t)=\frac{1}{2}(a(t)+b(t))h(t)\times L\\\\\therefore V(t)=\frac{1}{2}(20+b(t))\times h(t)\times L[/tex]

Differentiating both sides with respect to time we get

[tex]\frac{dV(t)}{dt}=\frac{1}{2}b'(t)h(t)L+\frac{1}{2}(20+b(t))\times h'(t)L[/tex]

Applying values we have

[tex]b(t)=20+h(t)\\b'(t)=h'(t)[/tex]

Thus we have

[tex]\frac{dV(t)}{dt}=\frac{1}{2}h'(t)h(t)L+\frac{1}{2}(20+20+h(t))\times h'(t)L\\\\2V'(t)=h'(t)L[h(t)+(40+h(t))]\\\\\therefore h'(t)=\frac{2V'(t)}{L(h(t)+(40+h(t)))}[/tex]

Applying values we get

[tex]h'(t)=0.075m/min=7.5cm/min[/tex]

Answer:

0.71 kg

Explanation:

L = length of the steel wire = 3.0 m

d = diameter of steel wire = 0.32 mm = 0.32 x 10⁻³ m

Area of cross-section of the steel wire is given as

A = (0.25) πd²

A = (0.25) (3.14) (0.32 x 10⁻³)²

A = 8.04 x 10⁻⁸ m²

ΔL = change in length of the wire = 1.3 mm = 1.3 x 10⁻³ m

Y = Young's modulus of steel = 20 x 10¹⁰ Nm⁻²

m = mass hanging

F = weight of the mass hanging

Young's modulus of steel is given as

[tex]Y = \frac{FL}{A\Delta L}[/tex]

[tex]20\times 10^{10} = \frac{F(3)}{(8.04\times 10^{-8})(1.3\times 10^{-3})}[/tex]

F = 6.968 N

Weight of the hanging mass is given as

F = mg

6.968 = m (9.8)

m = 0.71 kg

Answer: The mass of the object will be 11250 kg.

Explanation:

Density is defined as the mass contained per unit volume.

[tex]Density=\frac{mass}{Volume}[/tex]

Given :

Density of the object= [tex]12500kg/m^3[/tex]

Mass of object = ?

Volume of the object = [tex]0.9m^3[/tex]

Putting in the values we get:

[tex]12500kg/m^3=\frac{mass}{0.9m^3}[/tex]

[tex]12500kg/m^3=\frac{mass}{0.9m^3}[/tex]

[tex]mass=11250kg[/tex]

Thus the mass of the object is 11250 kg.

Answer:

The distance of the mosquito from the bat is 4.25 m.

Explanation:

Given that,

Speed of sound in air v= 340 m/s

Time t = 0.0250 second

Let d be the distance of the mosquito from the bat.

The distance traveled by the sound when the echo heard is 2d.

We need to calculate the distance

Using formula of  distance

[tex]v = \dfrac{2d}{t}[/tex]

Put the value into the formula

[tex]v = \dfrac{2d}{25\times10^{-3}}[/tex]

[tex]d =\dfrac{25\times10^{-3}\times340}{2}[/tex]

[tex]d=4.25\ m[/tex]

Hence, The distance of the mosquito from the bat is 4.25 m.

Utilizing the echo time of 0.0250 seconds and the sound speed of 340 m/s, the distance to the mosquito is calculated as 4.25 meters away from the bat.

Calculating the Distance to the Mosquito using Echo Time

To determine the distance to the mosquito that reflects the bat's shriek, we need to use the speed of sound in air and the echo time. Since the shriek's echo returns in 0.0250 seconds and the speed of sound is given as 340 m/s, we can calculate the total distance traveled by the sound (to the mosquito and back to the bat) with the equation:

Distance = Speed × Time

Here, the time is the round-trip time for the sound, so the distance to the mosquito is half the total distance:

Total Distance = 340 m/s × 0.0250 s = 8.5 m

Distance to the Mosquito = Total Distance / 2 = 8.5 m / 2 = 4.25 m

Therefore, the mosquito is 4.25 meters away from the bat.

Answer:

The distance to the first anti-nodal line is [tex]2.11\times10^{-3}\ m[/tex].

Explanation:

Given that,

Wavelength = 488 nm

Width [tex]d=6.23\times10^{-4}\ m[/tex]

Distance D =2.7 m

We need to calculate the distance to the first anti-nodal line

Using formula of the distance for first anti-nodal line

[tex]y_{n}=\dfrac{n\lambda D}{d}[/tex].....(I)

Where, n = number of fringe

d = width

D = distance from the screen

[tex]\lambda[/tex]=wavelength of light

Put the all value in the equation (I)

[tex]y_{n}=\dfrac{488\times10^{-9}\times2.7}{6.23\times10^{-4}}[/tex]

[tex]y_{n}=2.11\times10^{-3}\ m[/tex]

Hence, The distance to the first anti-nodal line is [tex]2.11\times10^{-3}\ m[/tex].

Answer:

1.85 x 10^10 cycles per second

Explanation:

B = 0.66 T, theta = 90 degree, q = 1.6 x 10^-19 C,

The time period of electron is given by

T = 2 π m / B q

Frequency is teh reciprocal of time period.

f = 1 /T

f = B q / (2 π m)

f = (0.66 x 1.6 x 10^-19) / (2 x 3.14 x 9.1 x 10^-31)

f = 1.85 x 10^10 cycles per second

Answer:

Speed of bullet = 389.61 m/s.

Explanation:

Considering the vertical motion of bullet

Initial vertical speed = 0 m/s

Vertical displacement = 2.9 cm = 0.029 m

Vertical acceleration = 9.81 m/s²

Substituting in s = ut + 0.5at²

    0.029 = 0 x t + 0.5 x 9.81 x t²

    t = 0.077 s

So ball hits the target after 0.077 s.

Now considering the vertical motion of bullet

Time = 0.077 s

Horizontal displacement = 30 m

Horizontal acceleration = 0 m/s²

Substituting in s = ut + 0.5at²

    30 = u  x 0.077 + 0.5 x 0 x 0.077²

     u = 389.61 m/s

Speed of bullet = 389.61 m/s.

Answer:

390 m/s

Explanation:

Let the horizontal speed be u.

Horizontal distance , x = 30 m

Vertical distance, y = 2.9 cm

Let time taken be t.

Use second equation of motion in vertical direction

H = uy × t + 1/2 gt^2

0.029 = 0.5 × 9.8 × t^2

t = 0.077 s

Horizontal distance = horizontal velocity × time

30 = u × 0.077

u = 390 m/s

Explanation:

The kinetic energy of an object is associated with its motion. Mathematically, it is given by :

[tex]E_k=\dfrac{1}{2}mv^2[/tex]........(1)

Where

m is the mass of the car

v is the velocity of the car

And the momentum of an object is equal to the product of mass and velocity i.e.

[tex]momentum(p)=mass(m)\times velocity(v)[/tex]..........(2)

From equation (1) and (2) it is clear that the kinetic energy and the momentum is directly proportional to the velocity of the object. As a car increases velocity, its kinetic energy or momentum increase faster.