Question 1

A soccer ball is kicked from the ground with an initial speed $$v_0 at an $$angle $$\$$alpha_0$$ above the horizontal. Neglecting air resistance, which of the following correctly gives the time it takes for the ball to reach its maximum height?

Accepted Answer

$$t = \frac{v_0$ \sin \$$alpha_0$$}{g}$$

Question 2

A car moves along a curved path at constant speed. Which statement about its acceleration is correct?

Accepted Answer

The acceleration is perpendicular to the velocity and points toward the center of curvature.

Question 3

A projectile is launched horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$Neglecting air resistance, what is the time it takes to hit the ground?

Accepted Answer

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

Question 4

Which of the following best describes the direction of the instantaneous velocity vector of a particle moving along a curved path?

Accepted Answer

It is always tangent to the path.

Question 5

A ball is thrown with initial velocity $$\vec{v}_0 at an $$angle $$\$$alpha_0$$ above the horizontal. What is the horizontal range R$ of the ball if it lands at the same height from which it was thrown (neglecting air resistance)?

Accepted Answer

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

Question 6

A cyclist rides east at $$5\ \mathrm{m/s}$$ while a train moves north at $$12\ \mathrm{m/s}. $$What is the magnitude of the velocity of the train relative to the cyclist?

Accepted Answer

$$\sqrt{5^2$ + 12^2$} = 13\ \mathrm{m/s}$$

Question 7

Which of the following is true about the acceleration of a particle in uniform circular motion?

Accepted Answer

It is always directed toward the center of the circle.

Question 8

A baseball is thrown horizontally from a height of $$20\ \mathrm{m}$$ with a speed of $$10\ \mathrm{m/s}. $$How far from the base of the building does it land? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\approx 20\ \mathrm{m}$$

Question 9

Which equation correctly gives the $$x-$$component of the instantaneous acceleration vector?

Accepted Answer

$$a_x = \frac{dv_x}{dt}$$

Question 10

A ball is dropped from rest and another is thrown horizontally from the same height at the same time. Neglecting air resistance, which statement is true?

Accepted Answer

Both balls hit the ground at the same time.

Question 11

A car is moving along a circular path and is slowing down. Which of the following best describes the direction of its acceleration?

Accepted Answer

It has a component toward the center and a component opposite to the direction of motion.

Question 12

A projectile is launched at an angle $$\$$alpha_0$$ with initial speed v_0$. What is the vertical component of its initial velocity?

Accepted Answer

$$v_{0y} = v_0$ \sin \$$alpha_0$$

Question 13

Which of the following is a correct statement about the effect of air resistance on projectile motion?

Accepted Answer

Air resistance decreases both the maximum height and the range.

Question 14

A particle moves in a circle of radius $$R at $$constant speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{R}$$

Question 15

A train moves at $$20\ \mathrm{m/s}$$ east relative to the ground. A passenger walks at $$2\ \mathrm{m/s}$$ north relative to the train. What is the magnitude of the passenger's velocity relative to the ground?

Accepted Answer

$$\sqrt{20^2$ + 2^2$} = \sqrt{404} \approx 20.1\ \mathrm{m/s}$$

Question 16

Which of the following best describes the path of a projectile in the absence of air resistance?

Accepted Answer

A parabola

Question 17

A particle's position is given by $$\vec{r}(t) = (4t^2$)\hat{i} + (3t)\hat{j}$$, where $$t is in $$seconds and position is in meters. What is the particle's velocity at $$t = 2\ \mathrm{s}$$?

Accepted Answer

$$\vec{v} = (16)\hat{i} + (3)\hat{j}\ \mathrm{m/s}$$

Question 18

A ball is thrown upward from a moving cart. The cart moves horizontally at constant velocity. What is the path of the ball as seen by an observer standing on the ground?

Accepted Answer

A parabola

Question 19

Which of the following is true about the velocity and acceleration vectors for a projectile at the peak of its trajectory (neglecting air resistance)?

Accepted Answer

The velocity is horizontal and the acceleration is vertical.

Motion in Two or Three Dimensions: Structured Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards