1) The distance is 12 km
2) The speed is 4 km/h
3) The displacement is 8.6 km at [tex]35.5^{\circ}[/tex] north of west
4) The velocity is 2.87 km/h at [tex]35.5^{\circ}[/tex] north of west
Explanation:
1)
The distance covered by an object is the total length of the path covered by the object during its motion, regardless of its direction. Distance is a scalar quantity.
In this problem, the person walks:
5 km North
and then
7 km west
So, the distance covered is:
d = 5 km + 7 km = 12 km
And being a scalar, distance has no direction.
2)
Speed is a scalar quantity that tells "how fast" an object is moving. It is defined as:
[tex]speed=\frac{d}{t}[/tex]
where
d is the distance covered
t is the time taken
In this problem, we have
d = 12 km is the distance
t = 3 h is the time taken
Substituting,
[tex]speed = \frac{12 km}{3h}=4 km/h[/tex]
And being a scalar, speed has no direction.
3)
Displacement is a vector quantity; it is a vector connecting the initial position to the final position of motion. Therefore, its magnitude must be found by using the rules of vectors.
In this problem, the person walks:
5 km North
and then
7 km West
The two motions are at right angle, so they form the sides of a right triangle, of which the hypothenuse corresponds to the displacement. Therefore, we can find it by using Pythagorean's theorem:
[tex]d=\sqrt{7^2+5^2}=8.6 km[/tex]
Being a vector, displacement has also a direction, given by:
[tex]\theta=tan^{-1}(\frac{5}{7})=35.5^{\circ}[/tex] north of west.
4)
Velocity is a vector quantity, given by:
[tex]velocity = \frac{d}{t}[/tex]
where
d is the displacement
t is the time taken
In this problem, we have
d = 8.6 km (displacement)
t = 3 h (time taken)
Therefore, the velocity is
[tex]v=\frac{8.6 km}{3 h}=2.87 km/h[/tex]
And being a vector, velocity has also a direction, which is the same of the displacement: so, [tex]35.5^{\circ}[/tex] north of west.
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The pilot of an airplane traveling 45 m/s wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped when the plane is how many meters from the island?
Answer:
254.56 mExplanation:
A object dropped from a plane from a certain height will follow a parabolic trajectory because it has a horizontal velocity equal to plane's velocity.
So, if supplies are to be dropped from a plane from a height of 160 m, let us calculate the time it takes to reach the ground.
[tex]H=\frac{1}{2}gt^{2}\\160=\frac{1}{2}\times10\times t^{2}\\t=\sqrt{32}=4\sqrt{2}\text{ }sec[/tex]
So, in this time, the supply moves a horizontal distance of [tex](4\sqrt{2}\text{ }sec)\times(45\text{ }\frac{m}{sec})=180\sqrt{2}\text{ }m=254.56\text{ }m[/tex].
∴ The supply must be dropped when the plane is 255 m away.
You push down on the car to provide more friction for the tires allowing the cars tires to propel it forward 5 meters. How much work do you do?
Answer:
The work done by you, W = 9800 J
Explanation:
Given data,
The displacement of the car, S = 5 m
Let the mass of the car be, m = 2000 kg
Let the coefficient of static friction be 0
Hence, no frictional force is acting on the tire and ground.
Let, you push down the car to provide more friction, μₓ = 0.1 (you can change the value)
In order to provide the static friction, you push down the car is equal to the static friction force,
Fₓ = μₓ · η
Where,
η - normal force acting on the car (mg)
Substituting the values,
Fₓ = 0.1 x 2000 x 9.8
= 1960 N
Therefore work done,
W = Fₓ x S
= 1960 N x 5 m
= 9800 J
Hence, the work done by you, W = 9800 J
Newton's First Law says that an object at rest will stay at rest, and an object in motion will stay in motion unless:
Question 1 options:
Acted on by a balanced force
Acted on by an unbalanced force
Acted on by equal forces in opposite direction
Acted on by multiple forces
Answer: Acted on by equal forces in opposite direction
Explanation:
Newton's First Law says that every body continue in its state of rest or constant speed on a straight line unless being acted upon by an external force.
Answer:
Acted on by equal forces in opposite direction
Explanation:
at what age u are a teens
Answer:
13 to 19 years old
Explanation:
Because these 6 years there is the word TEEN 13, 14, 15, 16, 17, 18, and 19. but in 20 there is no teen.
PLEASE MARK AS BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Show all work.
1. If an astronaut weighs 640 N on the earth's surface, what is the
gravitation force between him and the earth if he is 3 times the
distance from the Earth's surface?
The new gravitation force at the new location is 40 N
Explanation:
The weight of the astronaut is given by the equation
[tex]F=mg[/tex] (1)
where
m is the mass of the astronaut
g is the acceleration of gravity
The acceleration of gravity at a certain distance [tex]r[/tex] from the centre of the Earth is given by
[tex]g=\frac{GM}{r^2}[/tex]
where G is the gravitational constant and M is the Earth's mass. So we can rewrite eq.(1) as
[tex]F=\frac{GMm}{r^2}[/tex]
When the astronaut is on the Earth's surface, [tex]r=R[/tex] (where R is the Earth's radius), so his weight is
[tex]F=\frac{GMm}{R^2}=640 N[/tex]
Later, he moves to another location where his distance from the Earth's surface is 3 times the previous distance, so the new distance from the Earth's centre is
[tex]r'=3R+R=4R[/tex]
Therefore, the new weight is
[tex]F'=\frac{GMm}{(4R)^2}=\frac{1}{16}\frac{GMm}{R^2}=\frac{F}{16}[/tex]
Which means that his weight has decreased by a factor 16: therefore, the new weight is
[tex]F'=\frac{640}{16}=40 N[/tex]
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Final answer:
The gravitational force on the astronaut 3 times farther from the Earth's surface than the radius would be 40 N, as at this distance the gravitational force is reduced to 1/16th of its original value.
Explanation:
The question asks: If an astronaut weighs 640 N on the earth's surface, what is the gravitation force between him and the earth if he is 3 times the distance from the Earth's surface? This requires understanding of Newton's law of universal gravitation, which can be expressed as F = G(m1m2)/r², where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.
As the astronaut moves to a distance 3 times farther from the surface of the Earth, the distance (r) from the center of the Earth becomes 4r, because the initial distance from the surface to the center of the Earth (the radius of the Earth, or 1r) is included. According to the inverse-square law, if the distance increases by a factor of n, the force decreases by a factor of n2. Thus, at 3 times the distance from the surface, or 4 times the radius of the Earth, the gravitational force becomes 1/16th of what it was at the surface.
Therefore, the new gravitational force is 640 N / 16 = 40 N.
A tin can has a volume of 1000cm^3 and a mass of 100g . What mass of lead shot can it carry without sinking in water.
900 grams of lead can be added max to the tin so that it does not sink.
Explanation:
According to the Archimedes principle, an object will not sink in a medium until the density of the object exceeds the density of the medium.
The medium we have is water.
The density of medium(water) is given as ρ° = 1 g/cm³
Density of an object is simply its mass contained per unit volume.
Density = mass/volume
Volume of the tin = v = 1000 cm³
Mass of the tin = m = 100 g
Mass of lead that can be added without sinking = x
Total mass after adding lead in the tin = Mt = m + x
Total density after lead is added to the tin is given as:
ρt = (m+x)/v
Now, according to Archimedes principle, lead can be added to the tin until the density of tin is equal to the density of water.
ρt = ρ°
Mt/v = ρ°
(m + x)/v = ρ°
⇒ (100 + x)/1000 = 1
⇒ 100 + x = 1000
⇒ x = 1000 - 100
x = 900 g
Keyword: Archimedes principle
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1. A4-kg ball has a momentum of 12 kg m/s. What is the ball's speed?
Ap
124
C22 A swimmer with a mass of 75 kg dives off a raft with a mass of 500 kg. If the swimmer's speed is 4 m/s
immediately after leaving the raft, what is the speed of the raft?
HINT" The swimmer and raft start off as one combined mass and then separate.
- After colliding, two objects stick together and have a single velocity. Identify the type of collision.
Trelastic
1) The ball's speed is 3 m/s
2) The final speed of the raft is 0.6 m/s
3) The collision is inelastic
Explanation:
1)
The momentum of an object is given by
[tex]p=mv[/tex]
where
p is the momentum
m is the mass of the object
v is its velocity
For the ball in this problem we have:
p = 12 kg m/s
m = 4 kg
Solving for v, we find its velocity (and so its speed):
[tex]v=\frac{p}{m}=\frac{12}{4}=3 m/s[/tex]
2)
We can solve this part by applying the law of conservation of momentum: in fact, the total momentum of an isolated system (=no external forces) must be conserved. Therefore we can write:
[tex]p_i = p_f[/tex] (1)
where
[tex]p_i = 0[/tex] is the total initial momentum (the swimmer and the raft are at rest at the beginning)
[tex]p_f = mv + MV[/tex] is the total final momentum, where
m = 75 kg is the mass of the swimmer
M = 500 kg is the mass of the raft
v = 4 m/s is the final velocity of the swimmer
V is the final velocity of the raft
And substituting into (1) we find:
[tex]0=mv+MV\\V=-\frac{mv}{M}=-\frac{(75)(4)}{500}=-0.6 m/s[/tex]
Where the negative sign indicates that the raft moves in the opposite direction to the swimmer: so, the speed of the raft is 0.6 m/s.
3)
In a collision between two objects, if the system is isolated the total momentum of the system is always conserved during the collision. However, this is not true for the total kinetic energy: in fact, due to the presence of internal frictions, part of the kinetic energy can be converted into thermal energy or other forms of energy.
Therefore, there are two types of collision:
- Elastic collision: in an elastic collision, also the total kinetic energy of the objects is conserved
- Inelastic collision: in an inelastic collision, the total kinetic energy is not conserved. The most extreme case is the perfectly inelastic collision, in which the two objects stick together after the collision, and in this case there is the maximum loss of kinetic energy.
Since in this problem the two objects stick together, the collision is inelastic.
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One type of entrepreneurial business could be an online business, and the article
lists Amazon as an example. If you get a job tomorrow working at Amazon, does
that make you an entrepreneur? Why or why not?
Answer:
No you would not be an entrepreneur
Explanation:
An entrepreneur is someone who creates a business, and also organize the business affairs. The entrepreneur takes on the biggest financial risk.
Answer:
No, taking a job with Amazon does not make one an entrepreneur
Explanation:
An entrepreneur is an individual that sets up a business or businesses (with the aim of making profit). In any organization, the person or persons that start up the business or businesses are the entrepreneurs while the people employed are the employee of the business/businesses.
Entrepreneurs usually create jobs for the employee and not the other way round (even when the idea could come from the employee).
From the above, it can be deduced that a person who gets a job at Amazon is an employee while the owner of Amazon is the entrepreneur.
A weightlifter lifts a 1250-N barbell 2 m in 3 s.How much power was used to lift the barbell?
If you guys help with this, you WILL be marked as Brainliest.
PLEEAASEEEE
The power is 833.3 W
Explanation:
First of all, we need to calculate the work done in lifting the barbell, which is equal to the change in gravitational potential energy of the barbell:
[tex]W=(mg)h[/tex]
where
mg = 1250 N is the weight of the barbell
h = 2 m is the change in height
Substituting,
[tex]W=(1250)(2)=2500 J[/tex]
Now we can calculate the power, which is equal to the work done per unit time:
[tex]P=\frac{W}{t}[/tex]
where
W = 2500 J is the work done
t = 3 s is the time taken
Substituting,
[tex]P=\frac{2500}{3}=833.3 W[/tex]
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By applying a force of 55 N, a pulley system can lift a box with a mass of 20.0 kg. What
is the mechanical advantage of the pulley system?
The mechanical advantage of the pulley is 3.56
Explanation:
The Mechanical Advantage (MA) of a pulley system is given by
[tex]MA=\frac{Load}{Effort}[/tex]
where
Load is the weight of the object lifted
Effort is the force applied in input
For the pulley in this problem, we have:
Effort = 55 N
While the load is the weight of the box of mass m = 20.0 kg:
[tex]Load = mg = (20.0 kg)(9.8 m/s^2)=196 N[/tex]
Substittuing, we find the MA of the pulley:
[tex]MA=\frac{196}{55}=3.56[/tex]
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A 5kg rock is thrown off a cliff that is 20 meters high onto the beach. What was the ricks velocity when it hits the beach?
The final velocity of the rock is 19.8 m/s
Explanation:
The motion of the rock is a free fall motion (subjected only to the force of gravity), with constant acceleration [tex]g=9.8 m/s^2[/tex] towards the ground. Therefore, we can use the following suvat equation:
[tex]v^2-u^2=2as[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the vertical displacement
For the rock in this problem,
u = 0 (initial velocity is zero)
[tex]a=g=9.8 m/s^2[/tex]
s = 20 m (height of the cliff)
Solving for v,
[tex]v=\sqrt{u^2+2as}=\sqrt{0+2(9.8)(20)}=19.8 m/s[/tex]
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a cart accelerates at 2 m/s^2 when a force of 60 N is applied, what is the mass of the cart?
Answer:
30 kg
Explanation:
Newton's second law:
F = ma
60 N = m (2 m/s²)
m = 30 kg
Answer:
[tex]30\:g[/tex]
Explanation:
Isaac Newton's second law of motion
[tex]\displaystyle ma = F_{net}[/tex]
[tex]\displaystyle \frac{60}{2} = m \\ \\ 30 = m[/tex]
* Now, that bar above 18 is what is known as bar notation, indicating repetition in the digits.
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As a ship comes into view over the horizon the top appears before the rest of the ship how does this demonstrate the earth is spherical
Final answer:
The appearance of a ship's top first as it approaches the horizon shows the Earth's curvature, as the lower parts disappear first due to the spherical shape.
Explanation:
When a ship comes into view on the horizon, the top appears before the rest of the ship, demonstrating that the Earth is spherical. This is because as the ship sails away from an observer, the curvature of the Earth causes the lower parts of the ship to disappear from view first, much like it would drop behind a hill. This phenomenon, which mariners like Columbus would have been familiar with, is a direct consequence of the Earth's spherical shape.
The higher masts of the ship remain visible for a while longer because they are the last to dip below the horizon as the ship follows the Earth's curvature. This effect proves that the Earth is not flat because if it were, the entire ship would simply appear smaller but would stay in full view as it moves away.
Moreover, the use of lookouts in the ship's mastheads also illustrates the Earth's curvature. On a spherical Earth, lookouts posted higher up can see further over the horizon than those at deck level. Conversely, if the Earth were flat, there would be little to no advantage of having lookouts at higher positions.
a box weighing 155 N is pushed horizontally down the hall at constant velocity. the applied force is 83 n what is the coefficient of friction between the box and the floor
Answer:
μ = 0.535
Explanation:
On a level floor, normal force = weight.
N = W
Friction force = normal force × coefficient of friction.
F = Nμ
Substitute:
F = Wμ
83 = 155μ
μ = 0.535
Round as needed.
Cart A is moving at 2 m/s and cart b is at rest. After a perfectly elastic collision (cart A is stationary after the collisions), how fast will cart b move? Both carts have a mass of 1 kg
Answer:
2 m/s
Explanation:
A weightlifter is bench-pressing 710 N. He raises the weight 0.65m above his chest. How much work does he do with this lift?
The work done is 6958 J
Explanation:
The work done by the man to raise the weight is the equal to the increase in gravitational potential energy of the weight, so we can write:
[tex]W=mg \Delta h[/tex]
where
(mg) is the weight, with m being the mass and g the acceleration of gravity
[tex]\Delta h[/tex] is the change in height of the weight
In this problem, we have
mg = 710 N (weight)
[tex]\Delta h = 0.65 m[/tex]
Therefore, the work done is
[tex]W=(710)(9.8)=6,958 J[/tex]
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The work done is 461.5 J.
Explanation:
According to Kinetics, the work done is calculated as the product of force which has done work, and the displacement it has imposed. Hence,
[tex]\text {Work done}=F \times s[/tex]
In the problem, the given data, F = 710 N and s = 0.65 m
By applying the given values to the work done equation, we get as follows,
[tex]\text { Work done } = 710 \times 0.65 = 461.5 \mathrm{J}[/tex]
The unit is same as the energy, work done defines when 1 N force acts in a 1 m distance along the force’s direction.
What is centripental force?
Answer:
Centripetal force is the force that is necessary to keep an object moving in a curved path and that is directed inward towards the center of rotation.
Explanation:
Definition of centripetal force:
Centripetal force is the force that is necessary to keep an object moving in a curved path and that is directed inward towards the center of rotation.
Example of centripetal force
A string on the end of which a stone is whirled about exerts a centripetal force on the stone.
The diagram is shown below
Where
The centripetal forces acting towards the centre C that is [tex]\vec {AC}[/tex]
and the direction is from A to C.
And the stone is moving in a circular motion with center as C.
What is tan(16°)?
A. 0.96
B.0.16
C.0.39
D.0.29
Answer:
D. 0.29
Explanation:
Which chemical reaction absorbs energy
Answer:
endothermic reactions
Answer:
endothermic reactions
Explanation:
endothermic reactions means the reaction gets super hot while the surrounding area gets colder. (absorbs energy)
exothermic means the surrounding area gets hot while it gets colder. (releases energy)
Which of the following correctly describes the inflammatory reaction?
A.
Injured cells stimulate increase in neutrophils & macrophages- which leads to phagocytosis of foreign invaders- which stimulates bradykinin- which initiates the release of histamine- which causes pain, swelling, redness, & heat
B.
Injured cells stimulate histamine- which initiates the releases of bradykinin- which increases neutrophils & macrophages- leads to phagocytosis of foreign invaders- causes pain, swelling, redness, & heat
C.
Injured cells stimulate bradykinin- which initiates the release of histamine- which causes pain, swelling, redness, & heat- increases neutrophils & macrophages- leads to phagocytosis of foreign invaders
D.
Injured cells stimulate pain, swelling, redness, & heat- which initiates bradykinin- which stimulates the release of histamine- which increases neutrophils & macrophages- leads to phagocytosis of foreign invaders
Answer:
I think D.
Injured cells stimulate pain, swelling, redness, and heat- which initiates bradykinin-which stimulates the release of histamine- which increases neutrophils and macrophages- leads to phagocytosis of foreign invaders.
Answer:
Injured cells stimulate bradykinin- which initiates the release of histamine- which causes pain, swelling, redness, & heat- increases neutrophils & macrophages- leads to phagocytosis of foreign invaders
Explanation:
Took the test
A 60kg block innitially at rest is pulled to the right a long a horizontal force of12N. Find the speed of the block after it has moved 3M if the surface in contact have a coefficient of kinetic friction of 0.15
Answer:
The speed of the block after it has moved 3M if the surface in contact have a coefficient of kinetic friction of 0.15 is 1.7s m/sec
Explanation:
Given:
mass of the block = 6.0 kg
Force with which the block is pulled = 12 N
Kinetic friction \mu= 0.15
Distance travelled s = 3 m
To Find:
speed of the block after it has moved 3 metres =?
Solution :
W know that the friction formula is
[tex]f_k = \mu m g[/tex]
Substituting the values,
[tex]f_k = (0.15)(6)(10)[/tex]
[tex]f_k= 9 N[/tex]
Now Acceleration is Given by
[tex]a=\frac{F -f_k}{m}[/tex]
[tex]a=\frac{12 - 9}{60}[/tex]
[tex]a=\frac{3}{6}[/tex]
a= 0.5 [tex]m/s^2[/tex]
Initial velocity is u = 0
Also we know that,
[tex]v^2 - u^2=2as[/tex]
So the equation becomes
[tex]v^2 =2as[/tex]
[tex]v=\sqrt{2as}[/tex]
Substituting the values,
[tex]v=\sqrt{2as}[/tex]
[tex]v=\sqrt{2(0.5)(3)}[/tex]
[tex]v= \sqrt{3}[/tex]
v= 1.73 m/s
Light travels from crown glass (n=1:52) into air (n=1.00). The angle of refraction in
air is 60°. What is the angle of incidence in glass?
The angle of incidence in glass is [tex]34.7^{\circ}[/tex]
Explanation:
We can solve this problem by applying Snell's law of refraction, which states that:
[tex]n_1 sin \theta_1 = n_2 sin \theta_2[/tex]
where
[tex]n_1, n_2[/tex] are the index of refraction of the first and second medium, respectively
[tex]\theta_1, \theta_2[/tex] are the angle of incidence and refraction, respectively
In this problem we have:
[tex]n_1 = 1.52[/tex] is the index of refraction of the first medium (glass)
[tex]n_2 = 1.00[/tex] is the index of refraction of the second medium (air)
[tex]\theta_2 =60^{\circ}[/tex] is the angle of refraction in glass
Solving for [tex]\theta_i[/tex], we find the angle of incidence:
[tex]\theta_1 = sin^{-1} (\frac{n_2 sin \theta_2}{n_1})=\sin^{-1}(\frac{(1.00)(sin 60^{\circ})}{1.52})=34.7^{\circ}[/tex]
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Final answer:
Using Snell's Law and the given indices of refraction for crown glass and air, as well as the angle of refraction in air, the angle of incidence within the crown glass is calculated to be approximately 41.14°.
Explanation:
To find the angle of incidence in glass when a ray of light exits the glass into air with a known angle of refraction, we use Snell's Law, which states that n1
*sin(θ1) = n2
*sin(θ2), where n1 and n2 are the refractive indices of the glass and air respectively, and θ1 and θ2 are the angles of incidence and refraction respectively. Given that the refractive index of crown glass is 1.52 (n1 = 1.52) and air is 1.00 (n2 = 1.00), with an angle of refraction of 60° in air (θ2 = 60°), we can rearrange Snell's Law to solve for the angle of incidence (θ1).
First, we plug in our known values:
1.52
*sin(θ1) = 1.00
*sin(60°)
Calculating the sine of 60 degrees and dividing by the refractive index of crown glass gives us the sine of the angle of incidence:
sin(θ1) = (1.00/1.52)
* sin(60°)
sin(θ1) ≈ 0.657
Using the inverse sine function, we find:
θ1 ≈ sin^−1(0.657)
θ1 ≈ 41.14°
Therefore, the angle of incidence in the crown glass is approximately 41.14°.
. Which is the transfer of energy as waves moving through space?
conduction
insulation
convection
radiation
Answer:
Radiation is the answer to your question
You throw a ball upward with a speed of 14m/s. What is the acceleration of the ball after it leaves your hand? Ignore air resistance and provide an explanation for your answer.
The acceleration of the ball after leaving the hand is [tex]9.8 m/s^2[/tex] downward
Explanation:
In order to find the acceleration of the ball during its motion, we have to study which forces are acting on it.
After the ball leaves the hand, if we neglect air resistance, there is only one force acting on the ball: the force of gravity, whose magnitude is
[tex]F=mg[/tex]
where m is the mass of the ball and g is the acceleration of gravity ([tex]g=9.8 m/s^2[/tex]), acting in the downward direction.
According to Newton's second law, the acceleration of the ball is given by
[tex]a=\frac{\sum F}{m}[/tex]
where
[tex]\sum F[/tex] is the net force acting on the ball
After the ball leaves the hand, the only force acting on it is the force of gravity, so we can substitute (mg) into the previous equation:
[tex]a=\frac{mg}{m}=g=9.8 m/s^2[/tex]
This means that the acceleration of the ball remains [tex]9.8 m/s^2[/tex] downward for the entire motion, after leaving the hand.
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Final answer:
The acceleration of the ball after it is thrown upward is a constant 9.8 m/s^2 downward due to gravity.
Explanation:
After you throw a ball upward with a speed of 14m/s, the acceleration of the ball after it leaves your hand is determined by the force of gravity. Regardless of the initial speed given to the ball, once it is not in contact with your hand, there is no longer any force being applied to it in the upward direction. Therefore, the only force acting on it is the force of gravity pulling it back toward the Earth's surface.
This force causes the ball to have a constant downward acceleration of approximately 9.8 m/s2, which is the standard acceleration due to gravity near the Earth's surface (often represented by the symbol g).
A(n) _____ is a high energy electron.
Question 2 options:
beta particle
helium nucleus
alpha particle
positron
An beta particle is a fast-moving electron.
An alpha particle and a helium nucleus are the same thing . . . a package composed of two protons and two neutrons.
An positron is a particle with the same mass as an electron but a positive charge.
Will give brainliest to the correct answer.
Answer:
The acceleration of the car is [tex]1.432 m/s^{2}[/tex]
Explanation:
We are assuming rightward coordinate positive and all quantities are along this direction
We know,
[tex]a = \frac{dv}{dt}[/tex]
where a - acceleration, v=velocity, t=time and x=displacement
multiply by dx in both sides
[tex]adx = \frac{dv}{dt} dx[/tex]
but we know [tex]\frac{dx}{dt} = v[/tex]
Therefore,
[tex]adx = vdv[/tex]
Here we integrate both sides with proper limits
x ranges from 0 to 110 as v ranges from 29 to 34
p = 0, r = 110, q = 29, s = 34
[tex]a\int\limits^r_pdx = \int\limits^s_q {v} \, dv[/tex]
a is given as constant thus can be pulled out of the integration
[tex]a[110-0] = [\frac{34^{2}}{2}- \frac{29^{2}}{2}][/tex]
Therefore,
Accelaration of the car is [tex]1.432 m/s^{2}[/tex]
Note:
Here moving to the right doesn't mean anything significant other than the fact that all quantities are pointing in that direction. Therefore obtained acceleration is also towards the right
If you know equation of motion for constant acceleration as
[tex]v^{2} -u^{2} = 2as[/tex] you can plug in values in this equation to obtain value of a
v - final velocity
u - initial velocity
s - displacement
Which of the following diagrams represent a balanced force
A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field?
Answer:
2100 J
Explanation:
Work = force × distance
W = Fd
W = (140 N) (15 m)
W = 2100 J
Answer:
[tex]\displaystyle 2100\:J[/tex]
Explanation:
[tex]\displaystyle FD = W → 2100 = [15][140][/tex]
Force by Distance
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A hiker walks 1 km east, 2km north, 4 km east, then 6 km north. What is the distance and displacement of the hiker
Answer:
The distance the hiker walked is, d = 13 km
The displacement of the hiker is, S = 9.4 km
Explanation:
Given data,
The displacement of towards east, d₁ = 1 km
The displacement of towards north, d₂ = 2 km
The displacement of towards east, d₃ = 4 km
The displacement of towards north, d₄ = 6 km
The total distance the hiker walked
d = d₁ + d₂ + d₃ + d₄
= 1 + 2 + 4 + 6
= 13 km
The distance the hiker walked is, d = 13 km
The resultant displacement of the hiker, S
S = √( A² + B² + 2 A B cosФ)
Where,
A = d₁ + d₃ = 5 km
B = d₂ + d₄ = 8 km
Ф = angle between A and B = 90°
Substituting in the displacement equation
S = √( 5² + 8²)
= 9.4 km
Hence, the displacement of the hiker is, S = 9.4 km
A 3kg Snickers candy bar is dropped of the top of the Washington Monument. If the
Monument is 170m tall, how fast does the Snickers hit the ground?
The final velocity of the candy is 57.7 m/s
Explanation:
The motion of the candy is a free fall motion, since it is subjected only to the force of gravity, so it is a uniformly accelerated motion and therefore we can use the following suvat equation:
[tex]v^2-u^2=2as[/tex]
where
v is the final velocity
u is the initial velocity
[tex]a=g=9.8 m/s^2[/tex] is the acceleration of gravity
s is the vertical displacement
In this problem, we have:
u = 0 (the candy is dropped from rest)
s = 170 m (the vertical displacement is the height of thr monument)
Solving for v, we find the velocity of the candy as it hits the ground:
[tex]v=\sqrt{u^2+2as}=\sqrt{0+2(9.8)(170)}=57.7 m/s[/tex]
Learn more about free fall motion:
brainly.com/question/1748290
brainly.com/question/11042118
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