Q: A ball is dropped from rest from a 100 m tall building. Ignoring air resistance, what is the velocity of the ball just before it hits the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 100} = 44.3\ \mathrm{m/s}$$

Q: A rock is dropped from a bridge and takes 2.5 s to hit the water below. What is the height of the bridge? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\Delta y = v_{0y} t + \frac{1}{2} a t^2$ = 0 + 0.5 \times 9.8 \times (2.5)^2$ = 30.6\ \mathrm{m}$$

Question 1

A ball is dropped from rest from a 100 m tall building. Ignoring air resistance, what is the velocity of the ball just before it hits the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 100} = 44.3\ \mathrm{m/s}$$

Question 2

Which of the following statements about objects in free fall near Earth's surface is correct?

Accepted Answer

All objects accelerate downward at $$9.8\ \mathrm{m/s^2$}$$ regardless of their mass.

Question 3

A rock is thrown straight up from the edge of a building and lands in the street below. If the building is 50 m tall and the rock is thrown upward at $$10\ \mathrm{m/s}$$, how long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Solve $$\Delta y = v_{0y} t + \frac{1}{2} a t^2$ with $$\Delta y = -50\ \mathrm{m}$$, v$$_{0y} = 10\ \mathrm{m/s}$$, a = -9.8$$\ \mathrm{$$m/s^2$$}$$: t$$ \approx 4.0\ \mathrm{s}$$

Question 4

Which equation would you use to find the displacement of an object in vertical free fall if you know the initial velocity, time, and acceleration?

Accepted Answer

$$\Delta y = v_{0y} t + \frac{1}{2} a t^2$

Question 5

A student throws a set of keys vertically upward to a friend in a window 4.0 m above. If the keys are caught 1.50 s later, what was their initial velocity? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Use $$\Delta y = v_{0y} t + \frac{1}{2} a t^2$; 4.0 = v$$_{0y} (1.5) - 0.5 	imes 9.8 	imes $$(1.5)^2$$; $$v_{0y} = 7.7\ \mathrm{m/s}$$

Question 6

Which of the following is NOT a correct step in solving a motion with acceleration problem, according to the provided method?

Accepted Answer

Ignore the acceleration due to gravity if the object is moving upward.

Question 7

A ball is thrown downward from a height of 20 m with an initial velocity of $$5\ \mathrm{m/s}. $$What is its velocity just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_{fy}^2 = v_{0y}^2 + 2 a \Delta y$$; $$v_{fy} = \sqrt{5^2$ + 2 	imes 9.8 	imes 20} = 20.2\ \mathrm{m/s}$$

Question 8

If an object is thrown vertically upward with an initial velocity $$v_{0y}$$, what is its velocity at the highest point of its trajectory?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 9

A rock is dropped from a bridge and takes 2.5 s to hit the water below. What is the height of the bridge? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta y = v_{0y} t + \frac{1}{2} a t^2$ = 0 + 0.5 	imes 9.8 	imes (2.5)^2$ = 30.6\ \mathrm{m}$$

Question 10

Which of the following is the correct value and direction for the acceleration due to gravity near Earth's surface?

Accepted Answer

$$a = -9.8\ \mathrm{m/s^2$}$$, downward

Question 11

A ball is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$How long does it take to reach its maximum height? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \frac{v_{0y}}{g} = \frac{15}{9.8} = 1.53\ \mathrm{s}$$

Question 12

If a ball is thrown upward and returns to the same height from which it was thrown, which of the following is true about its velocity just before it returns?

Accepted Answer

It is equal in magnitude and opposite in direction to its initial velocity.

Question 13

Which kinematic equation is most appropriate to use if you know the initial and final velocities, acceleration, and want to find displacement, but do not know the time?

Accepted Answer

$$v_{fy}^2 = v_{0y}^2 + 2 a \Delta y$$

Question 14

A stone is thrown downward from a cliff with an initial velocity of $$8\ \mathrm{m/s}. If it $$takes 3 s to reach the ground, what is the height of the cliff? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta y = v_{0y} t + \frac{1}{2} a t^2$ = 8 	imes 3 + 0.5 	imes 9.8 	imes 9 = 24 + 44.1 = 68.1\ \mathrm{m}$$

Question 15

Which of the following best describes the motion of an object in free fall?

Accepted Answer

It accelerates downward at a constant rate.

Question 16

A ball is thrown vertically upward with an initial velocity of $$20\ \mathrm{m/s}. $$What is the maximum height it reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_{fy}^2 = v_{0y}^2 + 2 a \Delta y$$; $$0 = 400 + 2(-9.8)\Delta y$$; $$\Delta y = \frac{400}{19.6} = 20.4\ \mathrm{m}$$

Question 17

If an object is thrown downward with an initial velocity, which of the following is true about its acceleration during its fall (ignoring air resistance)?

Accepted Answer

Its acceleration is constant and equal to $$-9.8\ \mathrm{m/s^2$}.$$

Question 18

A student drops a ball from a height $$h$$ and it takes $$t$$ seconds to reach the ground. Which equation correctly relates $$h$$, $$g$$, and $$t$$?

Accepted Answer

$$h = \frac{1}{2} g t^2$

Question 19

Which of the following is a correct assumption when using the UAM equations for free fall problems?

Accepted Answer

The acceleration is constant and equal to $$g.$$

Free Fall and Uniformly Accelerated Motion (UAM) in Physics

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