Question 1

A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector?

Accepted Answer

$$28\ \mathrm{km}$$

Question 2

A plane moving $$200\ \mathrm{m/s}$$ horizontally fires a projectile with speed $$50\ \mathrm{m/s} in a $$forward direction $$30.0^\circ$$ below the horizontal. What is the speed of the projectile with respect to a stationary observer on the ground?

Accepted Answer

$$293\ \mathrm{m/s}$$

Question 3

A swimmer heading directly across a river that is $$200\ \mathrm{m}$$ wide reaches the opposite bank in $$6.0\ \mathrm{min}. $$During this swim, she is swept downstream $$480\ \mathrm{m}. $$What is the speed of the current?

Accepted Answer

$$1.2\ \mathrm{m/s}$$

Question 4

Two perpendicular vectors $$\vec{A}$$ and $$\vec{B}$$ are added together giving vector $$\vec{C}. If $$the magnitudes of $$\vec{A}$$ and $$\vec{B}$$ are doubled without changing their directions, the magnitude of vector $$\vec{C}$$ will:

Accepted Answer

increase by a factor of $$4$$

Question 5

A velocity vector has components $$36\ \mathrm{m/s}$$ westward and $$22\ \mathrm{m/s}$$ northward. What are the magnitude and direction of this vector?

Accepted Answer

$$42\ \mathrm{m/s}$$, $$31.8^\circ$$ north of west

Question 6

A boat, whose speed in still water is $$8.0\ \mathrm{m/s}$$, crosses a river with a current of $$6.0\ \mathrm{m/s}. If $$the boat heads perpendicular to the current, what is the speed of the boat relative to an observer standing on the shore as it crosses the river?

Accepted Answer

$$10.0\ \mathrm{m/s}$$

Question 7

A plane has an airspeed of $$200\ \mathrm{m/s}$$ northward, and is in a wind of $$50.0\ \mathrm{m/s} to $$the west. The plane's speed relative to the ground is:

Accepted Answer

$$206\ \mathrm{m/s}$$

Question 8

Vector $$\vec{A}$$ has a magnitude of $$6.0\ \mathrm{m}$$ and points $$30^\circ$$ north of east. Vector $$\vec{B}$$ has a magnitude of $$4.0\ \mathrm{m}$$ and points $$30^\circ$$ west of north. The resultant vector $$\vec{A} + \vec{B} is $$given by:

Accepted Answer

$$7.2\ \mathrm{m} at an $$angle of $$26^\circ$$ east of north

Question 9

Three forces, $$\vec{F}_1$$, $$\vec{F}_2$$, and $$\vec{F}_3$$, each of magnitude $$70\ \mathrm{N}$$, all act on an object as shown in the figure. The magnitude of the resultant force acting on the object is:

Accepted Answer

$$210\ \mathrm{N}$$

Question 10

If vector $$\vec{A}$$ has components $$A_x = 3.0$$ and $$A_y = -4.0$$, and vector $$\vec{B}$$ has components $$B_x = 3.0$$ and $$B_y = -8.0$$, what is the magnitude of vector $$\vec{C} = \vec{A} - \vec{B}$$?

Accepted Answer

$$7.2$$

Question 11

A player throws a football $$50.0\ \mathrm{m} at$$ $$61^\circ$$ north of west. What is the westward component of the displacement of the football?

Accepted Answer

$$24.2\ \mathrm{m}$$

Question 12

When rolled down a mountainside at $$7.0\ \mathrm{m/s}$$, the horizontal component of its velocity vector was $$1.8\ \mathrm{m/s}. $$What was the angle of the mountain surface above the horizontal?

Accepted Answer

$$75^\circ$$

Question 13

If $$\vec{A} \cdot \vec{B} = 0$$, then the vectors $$\vec{A}$$ and $$\vec{B}$$ are oriented:

Accepted Answer

perpendicular to each other

Question 14

Consider two vectors $$\vec{A}$$ and $$\vec{B}$$ shown in the figure. The difference $$\vec{A} - \vec{B} is $$best illustrated by:

Accepted Answer

choice (c)

Question 15

A plane flies directly from city A to city B, which are separated by $$2300\ \mathrm{mi}. $$From A to B, the plane flies into a $$65\ \mathrm{mi/h}$$ headwind. On the return trip from B to A, the wind velocity is unchanged. If the plane's airspeed (assumed constant) of the plane relative to the air (that is, the airspeed) is $$530\ \mathrm{mi/h}$$, what is the speed of the plane relative to the ground?

Accepted Answer

$$465\ \mathrm{mi/h}$$

Question 16

A displacement vector is $$34.0\ \mathrm{m} in $$length and is directed $$60.0^\circ$$ east of north. What are the northward and eastward components of this vector?

Accepted Answer

$$22.2\ \mathrm{m}$$ northward, $$29.4\ \mathrm{m}$$ eastward

Question 17

If a vector has components $$A_x \u003c 0$$ and $$A_y \u003c 0$$, then the angle that this vector makes with the positive x-axis must be in the range:

Accepted Answer

$$180^\circ to$$ $$270^\circ$$

Question 18

The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors.

Accepted Answer

False

Vectors and Kinematics: Study Notes for College Physics

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