8/13/2019 Physics 1 Vector Review Problems

1/7

1

Physics 111/121Vector Mini-Review Problems

(See last page for answers)

ContentsFOP 3-11, 3-18, 3-15, 3-21

FOP 5-6, 5-7FOP 7-6, 7-11

FOP 10-46, 12-19, 12-21, 12-25

8/13/2019 Physics 1 Vector Review Problems

2/7

2

Problem 3-11:A woman walks 250 m in the direction 30 east of north, then 175 m directly east. Find (a)

the magnitude and (b) the angle of her final displacement from the starting point. (c) Find the distance

she walks. (d) Which is greater, that distance or the magnitude of her displacement?

Problem 3-18: Here are two vectors:

What are (a) the magnitude and (b) the angle (relative toi ) of a? What are (c) the

magnitude and (d) the angle of b? What are (e) the magnitude and (f) the angle of a+ b ; (g) the

magnitude and (h) the angle of b - a; and (i) the magnitude and (j) the angle of a- b ? (k) What is the

angle between the directions of b - a and a- b ?

8/13/2019 Physics 1 Vector Review Problems

3/7

3

Problem 5-6: Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a

processing dock, exerting the forces shown in the figure. What is the asteroid's acceleration (a) in unit-

vector notation and as (b) a magnitude and (c) a direction?

Problem 3-15E: Vector a has a magnitude of 5.0 m and is directed east. Vector b has a

magnitude of 4.0 m and is directed 35 west of north. What are a) the magnitude and (b) the direction

of a + b ? What are (c) the magnitude and direction of b- a?

Problem 3-21: The two vectors aandbin the figurehave equal magnitudes of 10.0 m. Find (a) the x

component and (b) the ycomponent of their vector sumr, (c) the magnitude of r, and (d) the angler

makes with the positive direction of the xaxis.

http://showreference%28%27netget/?sid=wiley%27,%27fig3-29%27)http://showreference%28%27netget/?sid=wiley%27,%27fig3-29%27)

8/13/2019 Physics 1 Vector Review Problems

4/7

4

Problem 7-6 A floating ice block is pushed through a displacement d = (15 m)i- (12 m)jalong a

straight embankment by rushing water, which exerts a forceF = (210 N)i- (150 N)j on the block. How

much work does the force do on the block during the displacement?

Problem 5 - 7: There are two forces on the 2.0 kg box in the sketch but only one is shown. The figure

also shows the acceleration of the box. Find the second force (a) in unit-vector notation and as (b) a

magnitude and (c) a direction.

8/13/2019 Physics 1 Vector Review Problems

5/7

5

Prob 7-11: The figureshows three forces applied to a trunk that moves leftward by 3.00 m over a

frictionless floor. The force magnitudes are F1= 5.00 N, F2= 9.00 N, and F3= 3.00 N. During the

displacement, (a) what is the net work done on the trunk by the three forces and (b) does the kinetic

energy of the trunk increase or decrease? By how much?

Problem 10-46:Two 2.0 kg bodies, Aand B, collide. The velocities before the collision VA = 15i+ 30jand v

B= -10i+ 5.0j. After the collision, v

A= -5.0i+ 20j. All speeds are given in meters per second. (a)

What is the final velocity of B? (b) How much kinetic energy is gained or lost in the collision?

Problem 12-19: What are the magnitude and direction of the torque about the origin on a particle located

at coordinates (0, -4.0 m, 3.0 m) due to (a) force F1with components F1x= 2.0 N and F1y = F1z= 0, and

(b) force F2 with components F2x= 0, F2y = 2.0 N, and F2z= 4.0 N?

http://showreference%28%27netget/?sid=wiley%27,%27fig7-26%27)http://showreference%28%27netget/?sid=wiley%27,%27fig7-26%27)

8/13/2019 Physics 1 Vector Review Problems

6/7

6

Problem 12-21: ForceF= (-8.0 N)i+ (6.0 N)jacts on a particle with position vector r= (3.0 m)i+

(4.0 m)j. What are (a) the torque on the particle about the origin and (b) the angle between the

directions of rand F?

Problem 12-25:At a certain time, a 0.25 kg object has a position vector r= 2.0i- 2.0k, in meters. Atthat instant, its velocity in meters per second is v= -5.0i+ 5.0k, and the force in newtons acting on it is

F= 4.0j. (a) What is the angular momentum of the object about the origin? (b) What torque acts on it?

8/13/2019 Physics 1 Vector Review Problems

7/7

7

Physics 111/106Vector Mini-Review Problem Answers

for Physics 106 Students (11/2003)

3-11: a) 370 m b) 35.8o c) 425 m d) distance

3-18: a) 5 m b) -36.9o c) 10 m d) 53.1o e) 11.2 m

f) 26.6o g) 11.2 m h) 79.7o i) 11.2 m j) 100.3o

k) 180o

3-15: a) 4.3 m b) 50.4o c) 8 m d) 156o

3-21: a) 1.59 m b) 12.1 m c) 122 m d) 82.5o

5-6: a) a= 0.86i0.167jm/s/s b) a = 0.876 m/s/s c) 10.7o

5-7: a) F2= -32i + 21j N b) F2 = 38 N c) 213o

7-6: 4950 J

7-11: a) 1.5 J F2K increases by 1.5 J

10-46: a) 10i+ 15j m/s b) 6.08 J lost

12-19: a) 10 N.m @ 53o b) 22 N.m along negative x-axis

12-21: a) 50k N.m b) 90o rand Fare perpendicular

12-25: a) zero b) 8( i+ k) N.m