Q: A ladder leans against a wall, making an angle of $$28^\circ$$ with the wall. If the length of the ladder is $$5.0\ \mathrm{m}$$, what is the height $$h$$ above the ground where the ladder touches the wall?

$$h = 5.0 \times \sin(28^\circ) = 2.35\ \mathrm{m}$$

Q: A skydiver jumps from a balloon at $$39\ \mathrm{km}$$ altitude. Neglecting air resistance, how long does it take to fall to the ground if $$g = 10\ \mathrm{m/s}^2$$ and starting from rest?

$$t = \sqrt{\dfrac{2x}{g}} = \sqrt{\dfrac{2 \times 39,000}{10}} \approx 88.4\ \mathrm{s}$$

Question 1

A ladder leans against a wall, making an angle of $$28^\circ$$ with the wall. If the length of the ladder is $$5.0\ \mathrm{m}$$, what is the height $$h$$ above the ground where the ladder touches the wall?

Accepted Answer

$$h = 5.0 	imes \sin(28^\circ) = 2.35\ \mathrm{m}$$

Question 2

Two vectors $$\vec{A}$$ and $$\vec{B}$$ are added to form a vector $$\vec{C}. If$$ $$A^2$$ + $$B^2$$ = $$C^2$$, which statement must be true about $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A}$$ and $$\vec{B}$$ must be at right angles to each other.

Question 3

If two vectors $$\vec{A}$$ and $$\vec{B}$$ are added together and the magnitude of the resultant is $$A + B$$, what is the relationship between $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A}$$ and $$\vec{B}$$ are in the same direction.

Question 4

A honeybee leaves the hive and flies $$2\ \mathrm{km}$$ away before returning to the hive. What is the magnitude of the bee's displacement vector?

Accepted Answer

$$0\ \mathrm{km}$$

Question 5

A runner runs $$1600\ \mathrm{m}$$ due east, then turns around and runs halfway back in $$5$$ minutes. What is the magnitude of the runner's average velocity?

Accepted Answer

$$2.67\ \mathrm{m/s}$$

Question 6

A cat runs from point $$A to$$ $$B$$ ($$20\ \mathrm{m}$$), then from $$B to$$ $$C$$ ($$5\ \mathrm{m}) $$along a straight line in $$30\ \mathrm{s}. $$What is the cat's average speed?

Accepted Answer

$$0.83\ \mathrm{m/s}$$

Question 7

Which of the following is the correct formula for average acceleration $$\vec{a}$$?

Accepted Answer

$$\vec{a} = \dfrac{\vec{v} - \vec{v}_0}{t - t_0$}$$

Question 8

A drag racer deploys a parachute and slows from $$28\ \mathrm{m/s} to$$ $$13\ \mathrm{m/s} in$$ $$3.0\ \mathrm{s}. $$What is the average acceleration?

Accepted Answer

$$-5.0\ \mathrm{m/s}^2$$

Question 9

A car starts from rest and accelerates at $$10\ \mathrm{m/s}^2. $$What is its velocity after $$3\ \mathrm{s}$$?

Accepted Answer

$$30\ \mathrm{m/s}$$

Question 10

Which kinematic equation would you use to find the displacement $$x of an $$object with initial velocity $$u$$, constant acceleration $$a$$, and time $$t$$?

Accepted Answer

$$x = ut + \frac{1}{2} a t^2$

Question 11

A skydiver jumps from a balloon at $$39\ \mathrm{km}$$ altitude. Neglecting air resistance, how long does it take to fall to the ground if $$g = 10\ \mathrm{m/s}^2$$ and starting from rest?

Accepted Answer

$$t = \sqrt{\dfrac{2x}{g}} = \sqrt{\dfrac{2 	imes 39,000}{10}} \approx 88.4\ \mathrm{s}$$

Question 12

A motorcycle starts from rest and accelerates at $$2.0\ \mathrm{m/s}^2$$ for $$10\ \mathrm{s}$$, then immediately decelerates at $$-1.5\ \mathrm{m/s}^2$$ until it stops. What is the total distance traveled?

Accepted Answer

$$66.7\ \mathrm{m}$$

Question 13

Which of the following is NOT a correct unit for acceleration?

Accepted Answer

$$\mathrm{m/s}$$

Question 14

A car moves with constant acceleration. If its velocity doubles when the time doubles, what can you say about its acceleration?

Accepted Answer

The acceleration is constant.

Question 15

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$What is its velocity after $$2\ \mathrm{s}$$? (Take $$g = 10\ \mathrm{m/s}^2$$ downward.)

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 16

Which of the following statements about freely falling bodies is correct?

Accepted Answer

All objects fall with the same acceleration regardless of mass, if air resistance is negligible.

Question 17

A car accelerates from $$0 to$$ $$30\ \mathrm{m/s} in$$ $$3\ \mathrm{s}. $$What is its acceleration?

Accepted Answer

$$10\ \mathrm{m/s}^2$$

Question 18

If a vector $$\vec{B}$$ has the same magnitude as $$\vec{A}$$ but a different direction, what can be said about $$\vec{B}$$ compared to $$\vec{A}$$?

Accepted Answer

Their magnitudes are the same, but their directions aren't.

Question 19

How many vectors in the $$xy-$$plane have $$x$$ and $$y$$ components that are both positive?

Accepted Answer

One

Vectors, Motion, and Kinematics: Study Notes for Introductory Physics

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