Q: A ball is dropped from rest from a height of 1.20 m. Neglecting air resistance, how long does it take to hit the ground? Use $$a_y = -9.8\ \mathrm{m/s^2$}.$$

$$t = \sqrt{\frac{2 \times 1.20}{9.8}} \approx 0.495\ \mathrm{s}$$

Q: A small ball rolls horizontally off a table 1.20 m high and lands 1.47 m away. What was its initial horizontal velocity $$v_{ix}$$? (Neglect air resistance.)

$$v_{ix} = \frac{1.47}{\sqrt{\frac{2 \times 1.20}{9.8}}} \approx 2.97\ \mathrm{m/s}$$

Q: If a projectile lands at the same height from which it was launched, which equation gives the total time of flight $$T$$?

$$T = \frac{2 v_0$ \sin \theta}{g}$$

Q: A ball is thrown upward at $$23^\circ$$ and $$3\ \mathrm{m/s}. $$What is the formula for the horizontal distance it travels before landing, assuming it lands at the same height?

$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Question 1

A ball is dropped from rest from a height of 1.20 m. Neglecting air resistance, how long does it take to hit the ground? Use $$a_y = -9.8\ \mathrm{m/s^2$}.$$

Accepted Answer

$$t = \sqrt{\frac{2 	imes 1.20}{9.8}} \approx 0.495\ \mathrm{s}$$

Question 2

Which equation correctly describes the final position $$x_f of an $$object moving with constant acceleration $$a$$ from initial position $$x_i$$ and initial velocity $$v_i$$ after time $$t$$?

Accepted Answer

$$x_f = x_i + v_i t + \frac{1}{2} a t^2$

Question 3

A small ball rolls horizontally off a table 1.20 m high and lands 1.47 m away. What was its initial horizontal velocity $$v_{ix}$$? (Neglect air resistance.)

Accepted Answer

$$v_{ix} = \frac{1.47}{\sqrt{\frac{2 	imes 1.20}{9.8}}} \approx 2.97\ \mathrm{m/s}$$

Question 4

In projectile motion, what is the acceleration in the horizontal direction ($$a_x) $$after the projectile is launched?

Accepted Answer

$$a_x = 0$$

Question 5

A projectile is shot upward at an angle of $$23^\circ$$ with a speed of $$3\ \mathrm{m/s}. $$What is the initial vertical velocity $$v_{iy}$$?

Accepted Answer

$$v_{iy} = 3 \sin 23^\circ \approx 1.17\ \mathrm{m/s}$$

Question 6

If a ball is thrown horizontally from a table, which of the following statements is true about its initial vertical velocity $$v_{iy}$$?

Accepted Answer

$$v_{iy} = 0$$

Question 7

Which kinematic equation would you use to find the time it takes for a projectile to fall from a height $$h$$ with initial vertical velocity $$v_{iy}$$?

Accepted Answer

$$y_f = y_i + v_{iy} t + \frac{1}{2} a_y t^2$

Question 8

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its initial horizontal velocity $$v_{ix}$$?

Accepted Answer

$$v_{ix} = v_0$ \cos 	heta$$

Question 9

A ball is thrown downward from a height with initial vertical velocity $$v_{iy}. $$Which equation gives its final vertical velocity $$v_{fy}$$ after time $$t$$?

Accepted Answer

$$v_{fy} = v_{iy} + a_y t$$

Question 10

Which of the following best describes the motion of a projectile after it is launched (neglecting air resistance)?

Accepted Answer

It has constant horizontal velocity and constant downward acceleration.

Question 11

A ball is dropped from a height $$h$$ and takes $$t$$ seconds to reach the ground. If the height is quadrupled, how long will it take to reach the ground?

Accepted Answer

$$2t$$

Question 12

If a projectile lands at the same height from which it was launched, which equation gives the total time of flight $$T$$?

Accepted Answer

$$T = \frac{2 v_0$ \sin 	heta}{g}$$

Question 13

A projectile is launched horizontally from a cliff. Which statement is true about its horizontal velocity during flight (neglecting air resistance)?

Accepted Answer

It remains constant throughout the flight.

Question 14

A ball is thrown upward at $$23^\circ$$ and $$3\ \mathrm{m/s}. $$What is the formula for the horizontal distance it travels before landing, assuming it lands at the same height?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 15

Which of the following is NOT a correct assumption for ideal projectile motion?

Accepted Answer

Air resistance is significant.

Question 16

A ball is thrown horizontally from a table. Which variable is zero at the moment of release?

Accepted Answer

$$v_{iy}$$

Question 17

If a projectile is launched at $$45^\circ$$ with speed $$v_0$$, what is its maximum range $$R on $$level ground?

Accepted Answer

$$R = \frac{v_0$^2}{g}$$

Question 18

A ball is dropped from a table and another is thrown horizontally from the same height. Which hits the ground first?

Accepted Answer

Both hit the ground at the same time.

Question 19

Which equation would you use to find the final vertical position $$y_f of a $$projectile after time $$t$$?

Accepted Answer

$$y_f = y_i + v_{iy} t + \frac{1}{2} a_y t^2$

Kinematics and Projectile Motion: Study Notes for PHYSICS 115

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