Q: A projectile is launched at an angle $$\theta$$ above the horizontal with initial speed $$v_0. $$What is the time to reach the maximum height?

$$t = \dfrac{v_0$ \sin \theta}{g}$$

Q: The range $$R of a $$projectile launched from ground level with initial speed $$v_0 at $$angle $$\theta is $$given by:

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

Question 1

A ball is thrown upward from the top of a 50.0 m building with an initial speed of 15.0 m/s. What is the maximum height above the ground the ball reaches? (Assume $$g = 9.8 \ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$61.5 \ \mathrm{m}$$

Question 2

Which of the following best describes the acceleration of a projectile at the highest point of its trajectory (neglecting air resistance)?

Accepted Answer

It is directed downward with magnitude $$g.$$

Question 3

A package is dropped from an airplane flying horizontally at $$40.0 \ \mathrm{m/s} at an $$altitude of $$100 \ \mathrm{m}. $$How far ahead of the target should the package be released to land at the target? (Assume $$g = 9.8 \ \mathrm{m/s^2$}$$ and neglect air resistance.)

Accepted Answer

$$180.0 \ \mathrm{m}$$

Question 4

The position vector of a particle is given by $$\vec{r} = b t^2$ \hat{i} - c t \hat{j}$$, where $$b = 2.00 \ \mathrm{m/s^2$}$$ and $$c = 9.00 \ \mathrm{m/s}. $$What is the velocity vector at $$t = 4.00 \ \mathrm{s}$$?

Accepted Answer

$$\vec{v} = 16 \hat{i} - 9 \hat{j} \ \mathrm{m/s}$$

Question 5

A projectile is launched at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$What is the time to reach the maximum height?

Accepted Answer

$$t = \dfrac{v_0$ \sin 	heta}{g}$$

Question 6

Which of the following statements about projectile motion is correct (neglecting air resistance)?

Accepted Answer

The horizontal and vertical motions are independent of each other.

Question 7

A destroyer fires two shells at the same initial speed but at different angles to hit two enemy ships. Which ship is hit first (neglecting air resistance)?

Accepted Answer

The ship hit by the shell with the lower angle.

Question 8

If you set your car's cruise control to a constant speed and drive around a curve, is your car accelerating?

Accepted Answer

Yes, because the direction of velocity is changing.

Question 9

The range $$R of a $$projectile launched from ground level with initial speed $$v_0 at $$angle $$	heta is $$given by:

Accepted Answer

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

Question 10

A projectile is launched at an angle above the horizontal. At which point in its trajectory does it reach minimum speed (neglecting air resistance)?

Accepted Answer

At the highest point of the trajectory.

Question 11

A projectile is launched at an angle above the horizontal. At which point in its trajectory is the acceleration greatest (neglecting air resistance)?

Accepted Answer

The acceleration is the same (nonzero) at all points.

Question 12

The position of an object is given by $$\vec{r} = \dfrac{1}{2}(4 \ \mathrm{m/s^2$}) t^2$ \hat{i} + (9 \ \mathrm{m/s}) t \hat{j} + (100 \ \mathrm{m}) \hat{k}. $$What is the magnitude of the object's acceleration at any time?

Accepted Answer

$$4 \ \mathrm{m/s^2$}$$

Question 13

A projectile is shot from the edge of a cliff $$115 \ \mathrm{m}$$ above ground level with an initial speed of $$65.0 \ \mathrm{m/s} at an $$angle of $$35.0^\circ$$ above the horizontal. What is the vertical component of the initial velocity?

Accepted Answer

$$v_{0y} = 65.0 \sin 35.0^\circ \ \mathrm{m/s}$$

Question 14

Which of the following is the correct equation for the vertical position $$y of a $$projectile as a function of time $$t ($$assuming $$y_0 is $$the initial height and $$v_{0y} is $$the initial vertical velocity)?

Accepted Answer

$$y = y_0$ + v_{0y} t - \dfrac{1}{2} g t^2$

Question 15

A ball is thrown horizontally from a cliff with speed $$v_0. $$Which statement is true about the time it takes to hit the ground?

Accepted Answer

It is the same as if the ball were simply dropped.

Quantities of 2D Motion and Projectile Motion – Study Notes

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