Q: For a projectile launched at an angle $$\theta$$ with initial speed $$v_0$$, what are the correct expressions for the initial velocity components?

$$v_{0x} = v_0$ \cos \theta$$, $$v_{0y} = v_0$ \sin \theta$$

Question 1

Which of the following best describes how to find the average acceleration vector between two velocity vectors $$\vec{v}_i$$ and $$\vec{v}_f$$?

Accepted Answer

Draw $$\vec{v}_i$$ and $$\vec{v}_f$$ tail-to-tail, then draw the vector from the tip of $$\vec{v}_i to $$the tip of $$\vec{v}_f$$; this is $$\Delta \vec{v}$$, and $$\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}.$$

Question 2

A ball rolls down a hill, through a valley, and up the other side. At the lowest point in the valley, which statement about the velocity $$\vec{v}$$ and acceleration $$\vec{a}$$ vectors is correct?

Accepted Answer

$$\vec{v}$$ and $$\vec{a}$$ are not necessarily parallel; $$\vec{a}$$ can have a component perpendicular to $$\vec{v}$$, changing the direction of motion.

Question 3

Which component of acceleration is responsible for changing the speed of an object in two-dimensional motion?

Accepted Answer

The parallel component $$\vec{a}_\parallel.$$

Question 4

For a projectile launched at an angle $$	heta$$ with initial speed $$v_0$$, what are the correct expressions for the initial velocity components?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$, $$v_{0y} = v_0$ \sin 	heta$$

Question 5

A projectile is launched from the ground with speed $$v_0 at an $$angle $$\$$theta_0$$. Neglecting air resistance, what is the time of flight until it returns to the same vertical level?

Accepted Answer

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

Question 6

Which of the following is true about the horizontal acceleration $$a_x of a $$projectile (neglecting air resistance)?

Accepted Answer

$$a_x = 0$$

Question 7

A car drives off a horizontal cliff of height $$h$$ with speed $$v_0. $$What is the horizontal distance $$x$$ from the base of the cliff where the car lands?

Accepted Answer

$$x = v_0$ \sqrt{\frac{2h}{g}}$$

Question 8

Two balls are released from the same height at the same time: one is dropped vertically, and the other is projected horizontally. Neglecting air resistance, which hits the ground first?

Accepted Answer

They hit the ground at the same time.

Question 9

The range $$R of a $$projectile launched from the ground with speed $$v_0 at $$angle $$\$$theta_0$$ is given by:

Accepted Answer

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

Question 10

At what launch angle $$\$$theta_0$$ is the range of a projectile maximized (for a given v_0$)?

Accepted Answer

$$\$$theta_0$$ = 45^\circ$$

Question 11

A projectile is launched from the ground. At the highest point of its trajectory, which statement is true?

Accepted Answer

The vertical component of velocity is zero.

Question 12

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

Accepted Answer

A parabola

Question 13

A 100 g ball and a 200 g ball roll off the same table with the same speed. Neglecting air resistance, which statement is true about the distance each lands from the base of the table?

Accepted Answer

Both land at the same distance.

Question 14

The maximum height $$h$$ reached by a projectile launched with speed $$v_0 at $$angle $$\$$theta_0$$ is:

Accepted Answer

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

Question 15

Which of the following is a correct statement about the independence of motion in projectile motion?

Accepted Answer

The horizontal and vertical motions are independent except for sharing the same time of flight.

Question 16

If a projectile is launched from the ground at $$v_0$$ and $$\$$theta_0$$, what is the equation for its vertical position y$ as a function of horizontal position x$?

Accepted Answer

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

Kinematics in Two Dimensions: Acceleration and Projectile Motion

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