Q: A ball is thrown straight upward with an initial velocity of $$v_0 = 15$$\ \mathrm{m/s}$$ from ground level. Neglecting air resistance, what is the maximum height reached by the ball? (Take g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

$$h_{max} = \dfrac{v_0$^2}{2g} = \dfrac{15^2$}{2 \times 9.8} = 11.5\ \mathrm{m}$$

Q: A ball is kicked straight up and returns to the ground after $$2.0\ \mathrm{s}. $$What was its initial speed? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$v_0 = g$$ \dfrac{t}{2} = 9.8 \times 1.0 = 9.8\ \mathrm{m/s}$$

Q: A student throws a ball upward from a balcony $$5\ \mathrm{m}$$ above the ground with an initial speed of $$8\ \mathrm{m/s}. $$How long does it take for the ball to hit the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Solve $$-5 = 8t - \dfrac{1}{2} \times 9.8 t^2$; t$$ \approx 1.63\ \mathrm{s}$$

Q: A ball is thrown downward with an initial speed of $$5\ \mathrm{m/s}$$ from a height of $$10\ \mathrm{m}. $$How long does it take to hit the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Solve $$-10 = 5t - \dfrac{1}{2} \times 9.8 t^2$; t$$ \approx 1.13\ \mathrm{s}$$

Question 1

A ball is thrown straight upward with an initial velocity of $$v_0 = 15$$\ \mathrm{m/s}$$ from ground level. Neglecting air resistance, what is the maximum height reached by the ball? (Take g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$h_{max} = \dfrac{v_0$^2}{2g} = \dfrac{15^2$}{2 	imes 9.8} = 11.5\ \mathrm{m}$$

Question 2

Which of the following best describes the acceleration of an object in free fall near Earth's surface (neglecting air resistance)?

Accepted Answer

It is constant and directed downward, $$a = -g$$

Question 3

Alice throws a ball downward from the top of a building, while Bill simply drops his ball from the same height. Which ball has the greater acceleration just after release?

Accepted Answer

Both balls have the same acceleration, $$a = -g$$

Question 4

A ball is kicked straight up and returns to the ground after $$2.0\ \mathrm{s}. $$What was its initial speed? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_0 = g$$ \dfrac{t}{2} = 9.8 	imes 1.0 = 9.8\ \mathrm{m/s}$$

Question 5

At the very top of its path, what are the velocity $$v$$ and acceleration $$a of a $$ball thrown straight upward?

Accepted Answer

$$v = 0$$, $$a = -g$$

Question 6

A ball is thrown upward with an initial speed of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is its speed when it returns to the thrower?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 7

Which of the following equations describes the position $$x of an $$object under constant acceleration $$a$$ starting from initial position $$x_0$$ and initial velocity $$v_0$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \dfrac{1}{2} a t^2$

Question 8

A ball is dropped from a height of $$20\ \mathrm{m}. $$How long does it take to reach the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}} = \sqrt{\dfrac{40}{9.8}} = 2.02\ \mathrm{s}$$

Question 9

Which graph best represents velocity $$v$$ versus time $$t$$ for an object in free fall (neglecting air resistance)?

Accepted Answer

A straight line with negative slope, $$v = v_0$ - g t$$

Question 10

A student throws a ball upward from a balcony $$5\ \mathrm{m}$$ above the ground with an initial speed of $$8\ \mathrm{m/s}. $$How long does it take for the ball to hit the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Solve $$-5 = 8t - \dfrac{1}{2} 	imes 9.8 t^2$; t$$ \approx 1.63\ \mathrm{s}$$

Question 11

Which of the following is a correct strategy for solving free-fall problems?

Accepted Answer

Identify the object, choose a coordinate system, list knowns and unknowns, apply relevant equations, and check units.

Question 12

If a ball is thrown upward and reaches its maximum height in $$t_{up}$$ seconds, how long does it take to return to the thrower?

Accepted Answer

$$2 t_{up}$$

Question 13

A ball is thrown downward with an initial speed of $$5\ \mathrm{m/s}$$ from a height of $$10\ \mathrm{m}. $$How long does it take to hit the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Solve $$-10 = 5t - \dfrac{1}{2} 	imes 9.8 t^2$; t$$ \approx 1.13\ \mathrm{s}$$

Question 14

Which of the following statements about free fall is correct?

Accepted Answer

All objects in free fall near Earth's surface experience the same acceleration, regardless of mass.

Question 15

A ball is thrown upward from ground level with an initial velocity $$v_0. $$What is its velocity at the same height on the way down?

Accepted Answer

$$-v_0$

Question 16

Which equation gives the velocity $$v of an $$object under constant acceleration $$a$$ after time $$t$$?

Accepted Answer

$$v = v_0$ + a t$$

Question 17

A ball is dropped from rest from a tall building. After $$3\ \mathrm{s}$$, what is its velocity? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = -g t = -9.8 	imes 3 = -29.4\ \mathrm{m/s}$$

Question 18

Which of the following best describes the position vs. time graph for an object in free fall?

Accepted Answer

A parabola opening downward (if upward is positive)

Physics 101: Free Fall and Constant Acceleration Study Notes

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