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VECTOR & RELATIVE VELOCITY
Set 1
1. What is the total displacement of a trip in which a person travels 10 km[N] and then 24 km[E]?
2. What is the total displacement of a trip of 50 km[W] followed by a trip of 100 km[N30°E]?
3. What is the total displacement of a trip of 100 km[N30°E] followed by a trip of 50 km[W]? What is
significant about the result when compared to the answer for question 2?
4. A small boy goes to a store 2 blocks[N], 3 blocks[E], l block[S], 5 blocks[W], 4 blocks[S] and then
2 blocks[E]. What is the total displacement of his trip?
Set 2
1. A baseball pitcher is warming up as he travels to a game by plane. The plane is flying at 400
km/h[W] relative to the ground. The pitcher throws a ball at 150 km/h relative to the airplane. What
is the ball's velocity relative to the ground, if the pitcher throws the ball towards
(a) The front of the plane?
(b) The rear of the plane?
2. A jet plane travelling horizontally at 1200 km/h relative to the ground fires a rocket forwards at
1100 km/h relative to itself. What is the velocity of the rocket relative to the ground?
3. A bowler is practising his game on a railway flatcar travelling at 50 km/h[N] relative to the ground.
If the ball's velocity relative to the flatcar is 60 km/h[S], what is its velocity relative to the ground?
4. A boat is travelling upstream at 5 km/h[N] relative to the shore. If there is a current of 7 km/h[S],
what is the boat's velocity relative to the water?
Set 3
1. A swimmer jumps into a river and swims straight for the other side at 1.5 km/h[N] relative to the
water. There is a current in the river of 2.0 km/h[W]. What is the swimmer's velocity relative to the
shore?
2. A conductor in a train travelling at 12.0 km/h[N] walks across the aisle at 5.0 km/h[E] relative to
the train. What is his velocity relative to the ground?
3. A mouse is crawling inside a cart that is being pushed across the deck of a moving boat. The mouse
is moving at 0.5 m/s[E] relative to the cart. The cart is travelling at l .2 m/s[E] relative to the
surface of the boat, and the boat is moving at 4.0 m/s[N] relative to the water. What is the velocity
of the mouse relative to the water?
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Set 4
1. A plane has a velocity of 300 km/h relative to the air. If the pilot points the plane straight north,
when there is a wind of 80 km/h blowing towards the west, what will the resultant velocity of the
plane be?
2. An airplane pilot checks her instruments and finds that the speed of the plane relative to the air is
325 km/h. The instruments also show that the plane is pointed in a direction [S3O°W]. A radio
report indicates that the wind velocity is 80 km/h[W]. What is the velocity of the plane relative to
the ground as recorded by an air traffic controller in a nearby airport?
3. A blimp pilot wants to travel north. The blimp can move at 26 km/h in still air. There is a wind of l0
km/h[E].
(a) What is the heading? (That is, which way should the pilot point the blimp?)
(b) How fast will the blimp travel relative to the ground?
4. An airplane pilot wants to fly east. The plane has a velocity of 500 km/h relative to the air. A wind
is blowing at 50.0 km/h[N]. Calculate
(a) The proper heading,
(b) The magnitude of the plane's velocity relative to the ground.
Set 5
1. A plane flying a triangular pattern flies l50 km[N], then 400 km[E].
(a) What is its total displacement after these two legs?
(b) What third displacement would complete the trip back to the starting point?
2. A boat sails 120 km[E60°N], then 60 km[W]. What is its displacement?
3. A balloon drifts 20 km[S60°E], then its engines are turned on and it flies 20 km[S60°W]. What is
its total displacement?
4. A man inside a plane flying at 400 km/h[W] fires a gun eastwards. The muzzle velocity of the gun
is 450 km/h. What is the velocity of the bullet relative to the ground?
5. A streetcar accelerates from rest at 2.5 m/s2[W]. A woman inside the streetcar is walking at 2.0
m/s[E] relative to the streetcar. What is her velocity relative to the ground at:
(a) 0 s? (b) 1.0 s? (c) 2.0 s? (d) 3.0 s? (e) 4.0 s?
6. A man is walking inside a railway boxcar at 3.0 m/s[N] relative to the boxcar. The boxcar is rolling
along a ferryboat at 5.0 m/s[S] relative to the ferryboat. The ferryboat is heading north at 4.0 m/s.
What is the velocity of the man relative to (a) the ferryboat? (b) the water?
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7. A boy and a girl both swim at 3.0 m/s. They jump into a river 1 .0 km across, with a current of 2.0
m/s[E].
(a) The boy faces due north at all times. What is his velocity relative to the ground?
(b) The girl swims so that she ends up directly across from her starting point. What is her
velocity relative to the ground?
(c) How many minutes does each take to cross the river?
(d) How far apart are the boy and girl when they reach the opposite bank?
8. A motorboat is headed [E30°N] with its engine set to move the boat at 30 km/h in still water. There
is a current of 1 5 km/h[S]. What is the velocity of the boat relative to the shore?
9. A boy in a car moving at 10 km/h[N] wants to throw a ball to a girl standing on the right-hand side
of the road. He is able to throw the ball at 20 km/h. He wants the ball to go straight east, directly to
her.
(a) Relative to the car, which way should he throw the ball in order to do this?
(b) Relative to the ground, how fast will the ball travel to reach her?
10. A pilot wants to fly north. The plane has an air speed of 350 km/h. There is a 25 km/h wind
blowing to the west.
(a) What is the plane's velocity relative to the ground?
(b) What is its heading?
11. A small plane is flying east at 100 km/h relative to the air, in a wind blowing at 20 km/h[S].
(a) What is the plane's speed relative to the ground?
(b) What is its track?
12. A pilot flies 300 km[E] and then back home 300 [W] at an air speed of 300 km/h. A 30 km/h wind
is blowing to the east.
(a) What is the pilot's velocity relative to the ground for each leg of the trip?
(b) What is the time for each leg of the trip, in minutes?
(c) How long, in minutes, would the trip take if there were no wind?
13. A ball rolls up a hill, starting at 10 m/s[up] and accelerating at 3.0 m/s2[down]. What is its velocity
after (a) 1.0 s? (b) 3.0 s? (c) 4.0 s?
14. A ship travels at 30 km/h[N30°E] for 10 h, and then at 20 km/h[W60°S] for 17 h. What is its total
displacement?
15. A man is standing on the deck of a freighter heading north at 10 km/h. He measures the wind
velocity and gets a reading of 10 km/h[E]. What is the actual wind velocity?
16. A pilot wants to fly a huge square path over the ground, 100 km[N], 100 km[W], 100 km[S], and
then 100 km[E]. Her plane has an air speed of 100 km/h. A 50 km/h wind is blowing to the south.
For each leg of the trip, calculate
(a) The ground speed,
(b) The heading,
(c) The time, in minutes.
(d) What would be the saving in time if there were no wind?
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17. A wheel with a radius of 50 cm is rolling along the ground at 10 m/s[E]. That is, the centre point of
the wheel is moving at 10 m/s[E].
(a) What are the velocities of the top, bottom, front, and back points of the wheel, relative to its
centre?
(b) What are the velocities of those four points relative to the ground?
ANSWERS
Set 1
1. 26 km[N67°E]
2. 87 km[N]
3.
4. 3 blocks[S]
2. 2.3 10 3 km/h
3. 10 km/h[S]
4. 12 km/h[N]
Set 3
1. 2.5 km/h[N53°W]
2. 13.0 km/h[N23°E]
3.
4. 12 km/h[N]
Set 4
1. 310 km/h[N15°W]
2. 338 km/h[W56°S]
3. (a) [N23°W]
(b) 24 km/h
5. (a) [E5.7°S]
(b) 497 km/h
2. 104 km[N]
3. 20 km[S]
4. 50 km/h[E]
6. (a) 2.0 m/s[S]
(b) 2.0 m/s[N]
7. (a) 3.6 m/s[N34°E]
(b) 2.2 m/s[N]
(c) 5.6 min, 7.6 min
(d) 670 m
8. 26 km/h[E]
9. (a) 349 km/h
(b) [N4.1°E]
10. (a) 102 km/h
(b) [E11°S]
13. 40 km[S30°W]
14. 14 km/h[E45°S]
11. (a) 330 km/h[E],
270 km/h[W]
(b) 55 min, 67 min
(c) 120 min
15. (a) 50 km/h, 87
km/h, 150 km/h, 87
km/h
(b) [N], [W30°N],
[S], [E30°N]
(c) 120 min, 69 min,
40 min, 69 min
(d) 58 min
Set 2
1. (a) 550 km/h[W]
(b) 250 km/h[W]
Set 5
1. (a) 427 km[N69°E]
(b) 427 km[W21°S]
5. (a) 2.0 m/s[E]
(b) 0.5 m/s[W]
(c) 3.0 m/s[W]
(d) 5.0 m/s[W]
(e) 8.0 m/s[S]
8. (a) [E30°S]
(b) 17 km/h
12. (a) 7.0 m/s[up]
(b) 1.0 m/s[up]
(c) 2.0 m/s[down]
16. (a) 10 m/s[E], 10 m/s[W],10 m/s[down], 10 m/s[up]
(b) 20 m/s[E], 0, 14 m/s[E45°down], 14 m/s[E45°up]