Q: A projectile is launched from the origin with initial speed $$v_0 at $$angle $$\$$theta_0$$. What is the equation for its trajectory y(x$$)$$?

$$y(x) = x \tan \$$theta_0$$ - \frac{g x^2$}{2 v_0$^2 \cos^2$ \$$theta_0$$}$$

Question 1

A cannonball is fired from the ground with an initial speed $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. Neglecting air resistance, what is the equation for the horizontal position x(t$$)$$ of the cannonball as a function of time?

Accepted Answer

$$x(t) = v_0$ \cos \$$theta_0$$ \cdot t$$

Question 2

A soccer ball is kicked with an initial velocity of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the vertical component of its initial velocity?

Accepted Answer

$$v_{0y} = 20 \sin 30^\circ$$

Question 3

Which of the following best describes the shape of the trajectory of a projectile (neglecting air resistance)?

Accepted Answer

A parabola

Question 4

A baseball is hit so that it leaves the bat with an initial speed of $$40.0\ \mathrm{m/s} at an $$angle of $$50^\circ. $$What is the time it takes to reach its maximum height? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t_h = \frac{40.0 \sin 50^\circ}{9.8}$$

Question 5

A projectile is launched from the ground with speed $$v_0 at $$angle $$\$$alpha_0$$. What is the formula for its maximum range R$?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2\$$alpha_0$$}{g}$$

Question 6

If a person walks at $$1.0\ \mathrm{m/s} on a $$train moving at $$3.0\ \mathrm{m/s} ($$both in the same direction), what is the speed of the person relative to the ground?

Accepted Answer

$$4.0\ \mathrm{m/s}$$

Question 7

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal velocity remains constant

Question 8

A ball is thrown horizontally from a cliff with speed $$v_0. $$Which equation gives the vertical position $$y(t)$$ after time $$t ($$assuming $$y=0 at $$the top)?

Accepted Answer

$$y(t) = -\frac{1}{2} g t^2$

Question 9

At what angle should a projectile be launched to achieve maximum range on level ground?

Accepted Answer

$$45^\circ$$

Question 10

A projectile is launched from the origin with initial speed $$v_0 at $$angle $$\$$theta_0$$. What is the equation for its trajectory y(x$$)$$?

Accepted Answer

$$y(x) = x 	an \$$theta_0$$ - \frac{g x^2$}{2 v_0$^2 \cos^2$ \$$theta_0$$}$$

Question 11

A football is kicked at $$v_0 = 25$$\ \mathrm{m/s}$$ at $$\$$theta_0 = 37$$^\circ$$. What is the maximum height reached by the football? (Use g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$h = \frac{v_0$^2 \sin^2$ \$$theta_0$$}{2g}$$

Question 12

A cyclist observes a passenger walking inside a train. Which equation correctly relates the velocities in the cyclist's frame ($$A$$), train's frame ($$B$$), and passenger ($$P$$)?

Accepted Answer

$$v_{A/P} = v_{B/P} + v_{A/B}$$

Question 13

A projectile is launched from the ground with speed $$v_0 at $$angle $$\$$theta_0$$. What is the total time of flight before it lands back on the ground?

Accepted Answer

$$t = \frac{2 v_0$ \sin \$$theta_0$$}{g}$$

Question 14

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

Accepted Answer

The horizontal velocity changes with time

Question 15

A stone is thrown from a cliff horizontally with speed $$v_0. $$How long does it take to hit the ground if the cliff is height $$h$$?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 16

A projectile is launched at $$v_0$$ and $$\$$theta_0$$. Which of the following gives the speed at the highest point?

Accepted Answer

$$v_0$$ \cos \$$theta_0$$

Projectile Motion and Relative Velocity: Physics with Calculus Study Notes

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