Q: Josh is climbing up a steep 34° slope, moving at a steady 0.75 m/s along the ground. How many meters of elevation does he gain in one minute?

$$\Delta y = 0.75 \times 60 \times \sin(34^\circ) = 25.1 \text{ m}$$

Q: A watermelon is dropped from a height of 10 m. How fast is it going when it hits the ground? (Assume $$g = 9.8\ \text{m/s}^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \text{m/s}$$

Question 1

A velocity vector is directed 40° above the positive x-axis and has a y-component of 10 m/s. What is the value of its x-component?

Accepted Answer

$$A_x = \frac{10}{\sin(40^\circ)}$$

Question 2

Josh is climbing up a steep 34° slope, moving at a steady 0.75 m/s along the ground. How many meters of elevation does he gain in one minute?

Accepted Answer

$$\Delta y = 0.75 	imes 60 	imes \sin(34^\circ) = 25.1 	ext{ m}$$

Question 3

A ball is thrown straight up into the air. What is the acceleration of the ball at the very top (maximum height)?

Accepted Answer

$$a = -g$$

Question 4

A rural mail carrier overshoots a mailbox, stops, shifts into reverse, and backs up until he is at the right spot. Which segment of the velocity graph represents the mail carrier moving backward?

Accepted Answer

The segment where $$v \u003c 0$$

Question 5

If it takes Harry 3.5 s to walk from $$x = -12 m to$$ $$x = -47 m$$, what is his velocity?

Accepted Answer

$$v = \frac{-47 - (-12)}{3.5} = -10 m/s$

Question 6

A chameleon's tongue accelerates at $$250\ 	ext{m/s}^2$$ for $$20\ 	ext{ms}$$, then travels at constant speed for another $$30\ 	ext{ms}. $$What is the total distance the tongue reaches?

Accepted Answer

$$d = \frac{1}{2} a t_1$^2 + v t_2$, where v = a$$ $$t_1$$

Question 7

A student throws ball A upward with speed $$v_0$$ and ball B downward with the same speed from the same height. Compare their accelerations immediately after leaving the hand.

Accepted Answer

Both balls have acceleration $$-g$$ downward

Question 8

A vector $$\vec{A}$$ has components $$A_x = 5$$, $$A_y = 2$$ and vector $$\vec{B}$$ has components $$B_x = -3$$, $$B_y = -5. $$What are the x- and y-components of $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$C_x = 2, C_y = -3$$

Question 9

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

Accepted Answer

$$v_{y,i} = v_i \sin 	heta$$

Question 10

A position-versus-time graph shows a straight line with positive slope. What does this indicate about the object's motion?

Accepted Answer

The object is moving at constant positive velocity

Question 11

A velocity-versus-time graph shows a straight line with negative slope. What does this indicate about the object's acceleration?

Accepted Answer

The object has constant negative acceleration

Question 12

A watermelon is dropped from a height of 10 m. How fast is it going when it hits the ground? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ 	ext{m/s}$$

Question 13

A vector has components $$A_x = 0$$ and $$A_y = 5. $$What is its magnitude?

Accepted Answer

$$A = \sqrt{A_x^2$ + A_y^2$} = 5$$

Question 14

A car moves at 15 m/s and a runner at 5 m/s, both in the same direction. What is the speed of the car relative to the runner?

Accepted Answer

$$v_{c/r} = v_{c/g} - v_{r/g} = 10\ 	ext{m/s}$$

Question 15

A dog moves according to the position graph shown in Figure P2.3. For how many seconds does the dog move at the slower speed?

Accepted Answer

From $$t = 0 to$$ $$t = 4 s$$, so 4 seconds

Question 16

Alan leaves Los Angeles at 8:00 AM to drive to San Francisco, 400 mi away, at 50 mph. Beth leaves at 9:00 AM and drives at 60 mph. Who gets to San Francisco first?

Accepted Answer

Beth arrives first

Question 17

A paramecium starts at the 65 mm mark and ends up at the 42 mm mark. What is its displacement?

Accepted Answer

$$\Delta x = x_f - x_i = 42 - 65 = -23\ 	ext{mm}$$

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