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1. A motorist traveled 60 km [S], then 35 km [N 45o E], and
finally 50 km [W].
a) Determine the total displacement of the motorist.
b) If the trip took 1.3 h, what was the average speed and average velocity for the trip?
2. A sparrow travels 10.0 km [N 45o E], 5.0 km [W], and then 2.0 km [S] in 2.5 h to get to a
bird feeder.
a) Determine the sparrow's displacement?
b) What would be the direction of the most direct return route for the sparrow?
c) If, while maintaining a constant speed equal to the average speed it had when going to
the bird feeder, the sparrow returns by the direct route, how long will the total trip take?
3. For each of the following, use a diagram to find either the sum or the difference vector.
4. What is the change in velocity for a UFO which changes velocity from 200 km/h [N] to
300 km/h [N 30o W].
5. A plane is flying at 100 m/s [E]. Determine the final velocity of the plane if the velocity changes
by 30 m/s [E 30o N].
6. A motorcycle is driven on a frozen lake. Vl and V2 are its initial and final velocities at times
3.0 s apart. The scale is 1 cm = 2.50 m/s. Use an accurate vector diagram to determine the
change in velocity. Also determine the average acceleration of the snowmobile?
7. A hockey puck moves at 30 m/s at an angle of 120o to its original path after being struck by a
stick. If the original velocity was 20 m/s [E] find its change in velocity.
8. Determine the horizontal and vertical components of the muzzle velocity of a cannon ball fired
at a speed of 100 m/s at an angle of 20o above the horizontal.
9. The shadow of an airplane moves across the ground at 200 km/h when the plane climbs at an
angle of 15o to the horizon. With the sun directly overhead,
a) Determine the air speed of the plane?
b) Determine how long it take to increase the airplane's altitude by 1000 m?
10. Determine the average velocity of a train which moves at a constant speed of 100 km/h east
for 40 min, then [N 30o E] for 20 min, and finally west for 30 min.
11. A stone is thrown downwards at an angle of 30o to the horizontal from the top of a cliff. If the
speed is 20 m/s, what are the horizontal and vertical components of the ball's starting velocity?
12. A stream flows west at 5.0 m/s. A boat, while keeping its bow pointing north, crosses the
stream traveling at 3.0 m/s with respect to the water. What is the resultant velocity of the
boat with respect to the shore?
13. An experimental flying platform rises with a uniform speed of 30 m/s at an angle of 50o to the
horizontal. Determine
a) the horizontal and vertical components of the velocity.
b) the time to reach a height of 1.00 km.
c) the distance moved horizontally while rising 1.00 km.
14. A 100 m wide river flows at 4.00 m/s[E]. A canoeist keeps her canoe pointing North while
paddling at 3.0 m/s with respect to the river. Determine
a) relative to the shore, the velocity of the canoe.
b) the crossing time.
c) how far down stream the boat is carried by the river.
15. Relative to city A, city B is 300 km[N 45o E] away. A north wind blows at 80 km/h.
Determine the airspeed and heading of an airplane if a flight between the cities takes 45 min.
16. A pilot keeps the nose of her plane pointed west. The plane's air speed is 900 km/h and the
wind is blowing from [N 45o E] at 300 km/h.
a) What is the heading of the plane with respect to the ground.
b) Determine the magnitude of the ground velocity.
c) Determine how long a flight of 500 km would take along the path in (a).
17. On the same shore of a river, located 10 km apart, are two boathouses. Person A walks on
the shore at a constant speed of 4.0 km/h from one boathouse to the other and then back again.
Person B paddles a canoe in the river from one boat house to the other and back again.
Person B can paddle at 4.0 km/h relative to the water. The water in the river is flowing at
2.0 km/h in the starting direction of the canoeist.
a) How much sooner than the walker does the canoeist reach the second boathouse?
b) Determine the round trip time for each.
18. A passenger walking on the deck of an ocean liner moving at 18 km/h [S], moves at 3.0 m/s
towards the back of the ship. After 12s, the passenger turns right and walks with the same
speed for 15 m to the rail.
a) With respect to the water, determine the passenger's velocity, while walking towards the
rear? While walking towards the rail?
b) Determine his resultant displacement relative to the water at the end of his walk by
mathematical means.
19. A pilot finds himself 150 km [W] and 40 km [S] of his starting point after flying for 30 min.
This was accomplished by maintaining a heading due west with an air speed of 240 km/h.
a) What is the wind velocity?
b) If he wishes to fly due west from his present position with the same air speed, what
heading should he now maintain?
22. Determine the acceleration of a puck which for an impact that lasts 0.03 s, changes velocity
from 10 m/s at an angle of 20o to the boards, to 8.0 m/s at 24o the boards.
23. A baseball moving horizontally at 15 m/s is struck by a batter. After being struck the ball moves
horizontally at 24 m/s, 40o to the left of the pitcher, the contact time of the ball and bat is
0.01 s. Determine
a) the change in velocity.
b) the ball's average acceleration during the contact time.
24. Determine the centripetal acceleration of a transport truck which travels around a circular
curve at 70 km/h if the radius of the curve is 250 m?
25. The centripetal acceleration on an airplane is 10 m/s2. If the plane is flying in a circle of radius
500m, how long will it take to complete one circumference?
26. An airplane takes 80 s to change its velocity from 1000 km/h [W] to 1000 km/h [E].
Calculate the average acceleration.
27. The second hand on a watch is 1.5 cm long from tip to the center. Determine
a) the speed of the tip of the hand.
b) at 15 s, at 45 s, and 60 s, the velocity of the tip of the hand.
c) the change in velocity from 30 s to 45 s.
d) average acceleration from 30 s to 45 s.
28. The centripetal acceleration of a truck is 8.3 m/s2. If the speedometer reads 90 km/h, what is
the radius of the curve?
29. Earth has a radius of 6.4 X 106 m. Determine the centripetal acceleration of an object on the
Earth's surface at the equator.
30. A homing pigeon has a uniform speed of 15 m/s while flying 800 m [N 37o E], then
300 m [W], and finally 400 m [E 37o S]. If a hawk flies in a straight line between the start
and finish points of the pigeon, what must the hawk's velocity be in order to leave and arrive at
the same time as the pigeon?
31. Two boys are at the same point on one side of a river, which is 40 m wide. The river current
is 1.0 m/s. The boys want to go to a point on the other shore directly opposite to where they
presently are. They both dive into the water at the same time. One of the boys swims
somewhat up stream so that his swimming velocity and the velocity of the river result in net
motion perpendicular to the shore of the river. The other boy keeps his body perpendicular to
the river current, and so he gets carried down stream. Once across the river, he runs at
6.0 m/s up stream to the desired point. Which boy arrives first, and how much does he beat
the other by?
32. A gun has a muzzle velocity of 300 m/s. If fired horizontally at a height of 1.5 m above the
ground, what is the range of the bullet?
33. A balloon is rising at a velocity of 5.15 m/s [72o to horizontal]. 9.8 m above the ground, a
bottle is dropped. Determine
a) the time for the bottle to hit the ground .
b) with respect to the balloon, the horizontal displacement of the bottle.
34. A ball rolling at 2 m/s rolls off or a table as shown. The three cameras take stroboscopic
photographs of the motion while the ball is in the air. Camera C is off to the side of the table.
Draw pictures showing what you think each camera's photograph will be like.
35. Determine the height of a window if it takes a ball 5.0 s to hit the ground when thrown
horizontally from the window at 10 m/s. Also calculate how far the ball lands from the base of
the building.
36. An artillery gun is located 44 m above the bottom of a large valley. The shell is fired at
245 m/s horizontally.
a) What is the flight time of the shell?
b) How far horizontally does the shell move before landing?
c) At the moment of impact, what is the magnitude of the vertical component of its velocity?
37. A bomber diving at an angle of 37o below horizontal, drops a bomb. The altitude at the
release point is 730 m. After 5.0 s the bomb hits the ground. Determine
a) the bomber's velocity.
b) the horizontal distance the bomb moved.
c) the vertical and horizontal components of the bomb's velocity at the moment of impact.
38. A football player kicks a ball with a velocity of 15 m/s at an angle of 42o above horizontal. A
second player starts running to catch the ball at the moment of the kick. If this player is 30 m
away when he starts running, how fast must he run in order to catch the ball?
November 19, 2013
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