Q: A projectile is launched with initial velocity $$\vec{v}_0 at $$angle $$\theta. $$What is the equation for its vertical velocity at time $$t$$?

$$v_y = v_0$ \sin \theta - g t$$

Question 1

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which equation correctly gives the horizontal component of its initial velocity?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$

Question 2

In projectile motion, which statement is true about the vertical acceleration of the projectile (neglecting air resistance)?

Accepted Answer

It is constant and equal to $$-g.$$

Question 3

A ball is thrown horizontally from a cliff. Which equation describes its vertical position as a function of time $$t$$?

Accepted Answer

$$y = y_0$ - \frac{1}{2} g t^2$

Question 4

Which component of acceleration changes the direction of an object's velocity in two-dimensional motion?

Accepted Answer

The perpendicular component $$\vec{a}_{\perp}$$

Question 5

A projectile is launched at an angle $$	heta$$ and lands at the same height from which it was launched. At what angle is the range maximized?

Accepted Answer

$$45^\circ$$

Question 6

A ball moves in uniform circular motion with radius $$r$$ and angular velocity $$\omega. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a_c = \$$omega^2$$ r$$

Question 7

If a car drives off a cliff horizontally at speed $$v_0$$ and lands a distance $$d$$ from the base, which equation would you use to find the time it takes to hit the ground?

Accepted Answer

$$y = y_0$ - \frac{1}{2} g t^2$

Question 8

A particle moves along a curved path in the $$xy-$$plane. Its instantaneous velocity vector is:

Accepted Answer

Always tangent to the trajectory.

Question 9

In uniform circular motion, what is true about the velocity and acceleration vectors?

Accepted Answer

Velocity is tangent to the circle; acceleration points toward the center.

Question 10

A projectile is launched with initial velocity $$\vec{v}_0 at $$angle $$	heta. $$What is the equation for its vertical velocity at time $$t$$?

Accepted Answer

$$v_y = v_0$ \sin 	heta - g t$$

Question 11

A ball is thrown horizontally from a height $$h. $$Ignoring air resistance, what is the shape of its trajectory?

Accepted Answer

A parabola

Question 12

Which formula gives the arc length $$s$$ traveled by a particle in circular motion, given radius $$r$$ and angular displacement $$	heta (in $$radians)?

Accepted Answer

$$s = r 	heta$$

Question 13

A Ferris wheel rotates at constant angular velocity $$\omega. $$What is the period $$T of $$one revolution?

Accepted Answer

$$T = 2\pi / \omega$$

Question 14

A cyclist moves at 5 m/s relative to the ground, while a car moves at 15 m/s in the same direction. What is the velocity of the cyclist relative to the car?

Accepted Answer

-10 m/s

Question 15

In two-dimensional motion, the average velocity vector $$\vec{v}_{avg}$$ between two points is:

Accepted Answer

$$\vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t}$$

Question 16

A ceiling fan slows from 60 rpm to rest in 25 s. What is the angular acceleration $$\alpha (in $$rad/s$$^2$$)? (1 rpm = $$2\pi/60$$ rad/s)

Accepted Answer

$$\alpha = -\frac{2\pi}{60} \div 25$$

Question 17

Which statement about projectile motion is correct?

Accepted Answer

The vertical and horizontal motions are independent, but share the same time interval.

Question 18

A particle moves in a circle of radius $$r at $$constant speed $$v_t. $$What is its tangential velocity in terms of angular velocity $$\omega$$?

Accepted Answer

$$v_t = \omega r$$

Question 19

A projectile is launched at $$v_0$$ and angle $$	heta. If $$the vertical displacement is zero, which factor does NOT affect the range?

Accepted Answer

Mass of the projectile

Kinematics in Two Dimensions: Motion in a Plane, Projectile and Circular Motion

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