Question 1

Jane walks 200 m at an angle of $$60^\circ$$ north of east from her starting point. What are the eastward (x) and northward (y) components of her displacement?

Accepted Answer

$$x = 173\ \mathrm{m},\ y = 100\ \mathrm{m}$$

Question 2

Sam walks 300 m due east, then 400 m due north. What is the magnitude of his net displacement?

Accepted Answer

$$500\ \mathrm{m}$$

Question 3

Which of the following best describes how to add two vectors $$\vec{A}$$ and $$\vec{B}$$ graphically?

Accepted Answer

Place the tail of $$\vec{B} at $$the tip of $$\vec{A}$$, then draw the resultant from the tail of $$\vec{A} to $$the tip of $$\vec{B}.$$

Question 4

A right triangle has an angle $$	heta$$ and sides labeled as adjacent, opposite, and hypotenuse. Which trigonometric function gives the ratio of the opposite side to the hypotenuse?

Accepted Answer

$$\sin	heta$$

Question 5

Loveland is 18 km due south of Fort Collins and 31 km due west of Greeley. What is the distance between Fort Collins and Greeley?

Accepted Answer

$$\sqrt{18^2$ + 31^2$}\ \mathrm{km}$$

Question 6

A car moves to the left with increasing speed. Which velocity vector diagram best represents this motion?

Accepted Answer

The velocity vectors point to the left and increase in length over time.

Question 7

A student walks east 0.55 km, then north 3.25 km. How far is the student from the starting point?

Accepted Answer

$$\sqrt{0.55^2$ + 3.25^2$}\ \mathrm{km}$$

Question 8

Given the position vs. time graph of a car that starts at $$x = 10\ \mathrm{km}$$, moves left to $$x = -20\ \mathrm{km}$$, stops, then returns to the origin, which statement is correct?

Accepted Answer

The car changes direction twice and stops once.

Question 9

A student’s position is measured every minute as they walk to school. If the position increases by 60 m each minute for the first 4 minutes, what is the student’s average velocity during this interval?

Accepted Answer

$$60\ \mathrm{m/min}$$

Question 10

If a car’s position remains unchanged for a period of time on a position vs. time graph, what does this indicate about the car’s motion?

Accepted Answer

The car is stopped.

Question 11

Which of the following is the correct formula for the magnitude of the displacement vector $$\vec{d}$$ between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 12

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

Accepted Answer

The object is moving at constant positive velocity.

Question 13

If a velocity vector points to the left and its length increases over time, what does this indicate about the object’s motion?

Accepted Answer

The object is moving to the left and speeding up.

Question 14

Which of the following best describes the displacement of a cow at $$-5$$ miles and a car at $$+4$$ miles relative to the post office at the origin?

Accepted Answer

The displacement between the cow and the car is $$9$$ miles.

Question 15

A student walks 0.55 km east and then 3.25 km north. What is the angle of their displacement vector relative to east?

Accepted Answer

$$	heta = \arctan\left(\frac{3.25}{0.55}ight)$$

Representing Motion and Vectors in Physics

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