Q: If a ball is dropped from rest and falls freely for $$3$$ seconds, what is its displacement? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$x = \frac{1}{2} \times 9.8 \times 3^2$ = 44.1\ \mathrm{m}$$

Q: A stuntman jumps from rest from a height of $$99.4\ \mathrm{m}$$ and lands in an airbag. Neglecting air resistance, what would be his speed on impact? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$v = \sqrt{2 \times 9.8 \times 99.4} = 44.1\ \mathrm{m/s}$$

Question 1

A ball is dropped from rest from the top of a building. Neglecting air resistance, what is the acceleration of the ball during its fall?

Accepted Answer

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

Question 2

Which of the following equations correctly relates the displacement $$x of an $$object under constant acceleration $$a$$ after time $$t$$, given initial velocity $$v_0$$?

Accepted Answer

$$x = v_0$ t + \frac{1}{2} a t^2$

Question 3

A stone is thrown vertically upward with an initial velocity of $$20\ \mathrm{m/s}. $$What is its velocity at the maximum height?

Accepted Answer

$$v = 0$$

Question 4

A skydiver jumps from rest from a plane. If air resistance is neglected, which kinematic equation would you use to find the velocity after falling for time $$t$$?

Accepted Answer

$$v = v_0$ + a t$$

Question 5

A ball is thrown downward from a height $$H$$ with initial velocity $$v_0. $$What is the velocity of the ball just before it hits the ground, neglecting air resistance?

Accepted Answer

$$v = \sqrt{v_0$^2 + 2 g H}$$

Question 6

A tennis ball is tossed straight up and reaches its maximum height. What is the acceleration of the ball at the highest point?

Accepted Answer

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

Question 7

A rock is dropped from a cliff and hits the ground after $$4$$ seconds. What is its velocity just before impact? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and initial velocity is zero.)

Accepted Answer

$$v = 39.2\ \mathrm{m/s}$$

Question 8

Which statement is true about the acceleration of a freely falling object in a vacuum?

Accepted Answer

It remains constant at $$-9.8\ \mathrm{m/s^2$}.$$

Question 9

A ball is thrown vertically upward with a speed of $$25.0\ \mathrm{m/s}. $$How long does it take to reach its highest point? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$t = \frac{25.0}{9.8} = 2.55\ \mathrm{s}$$

Question 10

If a ball is dropped from rest and falls freely for $$3$$ seconds, what is its displacement? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$x = \frac{1}{2} 	imes 9.8 	imes 3^2$ = 44.1\ \mathrm{m}$$

Question 11

A coin is tossed upward with an initial speed of $$5.0\ \mathrm{m/s}. $$What is the maximum height it reaches above its point of release? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{25}{19.6} = 1.28\ \mathrm{m}$$

Question 12

Which of the following is a catchword that implies the initial velocity $$v_0 = 0$?

Accepted Answer

"from rest"

Question 13

A stuntman jumps from rest from a height of $$99.4\ \mathrm{m}$$ and lands in an airbag. Neglecting air resistance, what would be his speed on impact? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v = \sqrt{2 	imes 9.8 	imes 99.4} = 44.1\ \mathrm{m/s}$$

Question 14

Which graph best represents the vertical velocity of an arrow as a function of time when launched straight up and then falls back down, ignoring air resistance?

Accepted Answer

A straight line with negative slope crossing zero at the highest point

Question 15

If a ball is thrown upward and returns to the thrower's hand, what is its velocity just before it is caught (neglecting air resistance)?

Accepted Answer

Equal in magnitude and opposite in direction to its initial velocity

Question 16

Which of the following statements about free fall is correct?

Accepted Answer

The acceleration is always downward and constant

Question 17

A ball is thrown vertically upward with initial velocity $$v_0. $$Which equation gives the time to reach the maximum height?

Accepted Answer

$$t = \frac{v_0$}{g}$$

Question 18

A feather and a stone are dropped simultaneously in a vacuum. Which statement is true?

Accepted Answer

Both will hit the ground at the same time

Question 19

Which kinematic equation would you use to find the displacement of a freely falling object after time $$t$$, starting from rest?

Accepted Answer

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

Freely Falling Objects and Kinematics under Gravity

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