Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Which of the following correctly describes the horizontal and vertical components of its initial velocity?

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

Question 1

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following correctly describes the horizontal and vertical components of its initial velocity?

Accepted Answer

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

Question 2

A ball is thrown horizontally from a cliff. Ignoring air resistance, which statement is true about its motion?

Accepted Answer

The horizontal velocity remains constant, while the vertical velocity increases linearly with time.

Question 3

Which equation gives the displacement vector $$\Delta \vec{r}$$ between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$) in $$the $$xy-$$plane?

Accepted Answer

$$\Delta \vec{r} = (x_2$ - x_1$) \hat{i} + (y_2$ - y_1$) \hat{j}$$

Question 4

A stunt driver drives a car off a 10.0-m-high cliff at a speed of 20 m/s. How far from the base of the cliff does the car land? (Assume $$g = 9.8 m/s$^2$$ and ignore air resistance.)

Accepted Answer

About 45 m

Question 5

In projectile motion, which statement best describes the acceleration vector?

Accepted Answer

It points downward and is constant.

Question 6

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 7

Which of the following best describes the velocity vector of a particle in uniform circular motion?

Accepted Answer

It is tangent to the circle at every point.

Question 8

A Ferris wheel has a radius of 9.0 m and rotates 2.0 times per minute. What is the speed of a rider? (Use $$v = 2\pi r / T)$$

Accepted Answer

About 1.9 m/s

Question 9

Which formula gives the centripetal acceleration for a particle moving in a circle of radius $$r$$ with tangential speed $$v_t$$?

Accepted Answer

$$a_c = v_t^2$ / r$$

Question 10

A ceiling fan spinning at 60 rpm coasts to a stop in 25 s. How many revolutions does it make while stopping? (Hint: Use average angular velocity.)

Accepted Answer

About 12.5 revolutions

Question 11

In two-dimensional motion, the instantaneous velocity vector $$\vec{v} is $$given by:

Accepted Answer

$$\vec{v} = \frac{d\vec{r}}{dt}$$

Question 12

A ball is rolling down a hill, through a valley, and up the other side. At the lowest point in the valley, which component of acceleration is nonzero?

Accepted Answer

Only the perpendicular component $$a_{\perp}$$

Question 13

Which of the following is true about the independence of motion in projectile motion?

Accepted Answer

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

Question 14

A particle moves in a circle of radius $$r at $$constant angular velocity $$\omega. $$What is the period $$T of $$its motion?

Accepted Answer

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

Question 15

If a projectile is launched at $$	heta$$ and another at $$90^\circ - 	heta$$ with the same speed, what can be said about their ranges (assuming they land at the same height)?

Accepted Answer

Both projectiles will have the same range.

Question 16

In circular motion, what is the relationship between tangential velocity $$v_t$$ and angular velocity $$\omega$$?

Accepted Answer

$$v_t = \omega r$$

Question 17

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 18

Which of the following best describes the effect of the perpendicular component of acceleration $$a_{\perp} in $$two-dimensional motion?

Accepted Answer

It changes the direction of the object's velocity.

Question 19

A particle moves in a circle and its angular velocity increases with time. What is the sign of its angular acceleration $$\alpha if $$the rotation is counterclockwise?

Accepted Answer

Positive

Question 20

Which equation relates arc length $$s to $$radius $$r$$ and angle $$	heta (in $$radians) in circular motion?

Accepted Answer

$$s = r 	heta$$

Motion in Two Dimensions: Kinematics and Circular Motion

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