Q: A ball rolls horizontally off a table that is 1.20 m high and lands 1.47 m away from the edge. What was its initial speed as it left the table? Neglect air resistance.

$$v_{ix} = \frac{1.47}{\sqrt{2 \times 1.20 / 9.8}}$$

Q: For a ball shot upward at $$23^\circ$$ and $$3 m/s$$, which equation gives the time of flight before it lands (neglecting air resistance)?

$$t = \frac{2 v_0$ \sin \theta}{g}$$

Q: Which trigonometric function gives the ratio of the opposite side to the hypotenuse in a right triangle?

$$\sin \theta = \frac{\text{opp}}{\text{hyp}}$$

Q: A ball is thrown horizontally from a cliff. Which of the following best describes its initial velocity components?

$$v_{ix} \neq 0$$, $$v_{iy} = 0$$

Q: A ball is shot upward at $$23^\circ$$ and $$3 m/s. $$What is the horizontal distance it travels before landing? (Neglect air resistance)

$$d = v_0$ \cos \theta \cdot t$$

Question 1

A ball rolls horizontally off a table that is 1.20 m high and lands 1.47 m away from the edge. What was its initial speed as it left the table? Neglect air resistance.

Accepted Answer

$$v_{ix} = \frac{1.47}{\sqrt{2 	imes 1.20 / 9.8}}$$

Question 2

Which statement best describes the independence of motion in two dimensions?

Accepted Answer

Motion in the x direction is completely independent of motion in the y direction.

Question 3

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

Accepted Answer

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

Question 4

For a ball shot upward at $$23^\circ$$ and $$3 m/s$$, which equation gives the time of flight before it lands (neglecting air resistance)?

Accepted Answer

$$t = \frac{2 v_0$ \sin 	heta}{g}$$

Question 5

Which of the following is true for the acceleration of a projectile in flight (neglecting air resistance)?

Accepted Answer

Acceleration is $$9.8 m/s$^2$$ downward in the y direction and zero in the x direction.

Question 6

A car 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 7

Which kinematic equation correctly relates final position $$x_f to $$initial position $$x_i$$, initial velocity $$v_{ix}$$, and acceleration $$a_x$$ over time $$t$$?

Accepted Answer

$$x_f = x_i + v_{ix} t + \frac{1}{2} a_x t^2$

Question 8

If $$x(t) = 3t^2$ + 2t + 6$$, what is the instantaneous velocity $$v(t)$$?

Accepted Answer

$$v(t) = 6t + 2$$

Question 9

A ball is dropped (not thrown) from a height. What is its initial vertical velocity?

Accepted Answer

$$v_{iy} = 0$$

Question 10

Which trigonometric function gives the ratio of the opposite side to the hypotenuse in a right triangle?

Accepted Answer

$$\sin 	heta = \frac{	ext{opp}}{	ext{hyp}}$$

Question 11

If $$v_x = 3 m/s $$and $$v_y = 4 m/s$$, what is the magnitude of the velocity vector $$|v|$$?

Accepted Answer

$$|v| = 5 m/s$$

Question 12

Which statement about uniform circular motion is correct?

Accepted Answer

The speed remains constant, but the direction changes continuously.

Question 13

What is the period $$T of an $$object moving in a circle if its frequency is $$f$$?

Accepted Answer

$$T = \frac{1}{f}$$

Question 14

Given $$x(t) = 4t^3$ + 2$$, what is the acceleration $$a(t)$$?

Accepted Answer

$$a(t) = 12t$$

Question 15

Relative velocity between two objects moving in the same direction is given by:

Accepted Answer

$$v_{rel} = v_1$ - v_2$

Question 16

If the slope of a position vs. time graph at a given point is positive, what does this indicate about the object's motion?

Accepted Answer

The object is moving in the positive direction.

Question 17

A ball is thrown horizontally from a cliff. Which of the following best describes its initial velocity components?

Accepted Answer

$$v_{ix} 
eq 0$$, $$v_{iy} = 0$$

Question 18

Which component of acceleration changes the direction of motion in two-dimensional kinematics?

Accepted Answer

The perpendicular component

Question 19

A ball is shot upward at $$23^\circ$$ and $$3 m/s. $$What is the horizontal distance it travels before landing? (Neglect air resistance)

Accepted Answer

$$d = v_0$ \cos 	heta \cdot t$$

Motion in Two Dimensions and Projectile Motion: Study Notes for PHYSICS 371

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