Vectors Problem Packet Homework Solutions

(1-14)

7. A man walks 9 km east and then 15 km west. Find his distance traveled and his displacement.

d 9 km [E]

15 km [W]

d = 6 km [W]

Distance = 9 km + 15 km = 24 km

Added the vectors tip-to-tail

Scalar: No direction

Vector: direction and “little hat”

Resultant is d

R

100 mi/h

40 mi/h

= v

9. A robin is flying south for the winter at a rate of 40 miles per hour when it runs into a hurricane blowing due west at 100 miles per hour. What is the new velocity of the robin?

222 10040 R

smR 7.10710040 22

smsm

40100

tan

o6840

100tan 1

]68[7.107 WShkmv o

Find the resultant, which is the new

velocity.

Obviously, the robin was sped

up by the hurricane!!!

R

90 lbs [W]

210 lbs [Down]= F

10. Tarzan is hanging from one of his vines. His weight (his force) is 210 pounds, directed Southwards (actually, downward would be more appropriate). A boy sees that Tarzan wants to be pushed on his vine. The boy pushes with a force of 90 pounds West. The rope can withstand a 225-lb force. What happens to the “King of the Apes”? (Find both the magnitude and the direction of the resultant).

222 21090 R

lbR 5.22821090 22

lblb

21090tan

o2321090tan 1

]23[5.228 WDlbF o

Find the resultant, which is the force in

the vine.Since 228.5 lbs is greater than what the rope can take (225 lbs), Tarzan

will fall!

R

Worp 8 [E]

Worp 4 [N]

11. The world is again being attacked by hostile aliens from outer space. This looks like a job for Superman! With his super strength, he is able to fend off the attack. However, he wants to rid the earth of these dangerous aliens forever. As they fly away, they must pass close to our sun. They are heading on a bearing of East with a speed of Worp 8. If Superman can change their course to a bearing of between [N 61o E] and [N 64o E], they will crash into the sun. He gives them a velocity of Worp 4 on a bearing North. What happens? Has Good triumphed again?

worpsworps

84tan

o6.2684tan 1

]6.26[isdirection NE o

Since 61 < 63.4 < 64o, the world is safe!!!!!

]4.63[ EN oor ….

R

2500 N

1000 N

= F

12. On a television sports review show, a film clip is shown of the great tackle that ended the 1960 championship football game in Philadelphia. Jim Taylor of Green Bay was running forward down the field for a touchdown with a force of 1000 newtons (direction = South). Check Bednardek of Philadelphia runs across the field “at right angles to Taylor’s path” (direction = West) and tackles him with a force of 2500 newtons. Find the resultant of this crash.

222 10002500 R

NR 58.692,210002500 22

10002500tan

o6810002500tan 1

]68[693,2 WSNF o

Find the resultant, which is “resulting”

force.

What a hit!!!!!

13. A kite weighs 5 newtons (downward force). A girl throws the kite straight up in the air with a force of 20 newtons. If the wind is blowing horizontally with a force of 20 newtons EAST, find the new force acting upon it.

20 N

20 N

5 N

20 N

15 N

o9.362015tan 1

NF 252015 22

]37[25 upENF o

F

14. A clock has a minute hand that is 15 in long. Find: - the average speed of the minute hand’s tip.

- the inst. speed of the minute hand’s tip as it passes the 3 on the clock. - the displacement of the minute hand’s tip in moving from 1:30 to 1:45.

timedistancespeed

ininR 2.94)15(22distance

sec3600 min 60 hour1time

sin026.

sec3600in94.2speed

The minute hand’s speed is constant!!! Thus, the instantaneous

speed equals .026 m/s

15

15

d

]45[215 upleftd

45o

45 – 45 – 90 Triangle