Physics 12 Vectors Work Sheet
Final Review
Name:___________________
1) An airplane maintains a heading of due south at an airspeed (the speed at which the air passes past the
plane’s outer surface) of 540 mi/hr. It is flying through a jet stream which is moving east at 250mi/hr.
a) In what direction is the plane moving with respect to the ground?
b) What is the plane’s ground speed (speed with respect to the ground)?
c) What distance over the ground does the plane travel in 15 min.?
2) An airplane is flying toward a destination 200 miles due east of its starting point. There is a wind from
the northwest at 30 mi/hr. The pilot wishes to make the trip in 40 min.
a) What should be the heading?
b) At what airspeed should he fly?
3) What is the magnitude of a displacement whose components along the x, y, and z axes are respectively
4.00m, 2.50m, and 8.50m?
4) A steamer is traveling directly south at 25 km/hr in an area where the wind is from the southwest at 18
km/hr. What is the angle from the north of the smoke trail from the stack? (This is a challenge
problem for all you hot shots. Note that the question is talking about the direction of the stream of
smoke not the direction of the steamer.)
5) A man rows a boat “across” a river at 4.0 mi/hr. The boat is always kept headed at right angles to the
stream. The river is flowing at 6.0 mi/hr and is 0.2 miles wide.
a) In what direction does his boat actually go relative to a point directly across the stream?
b) How long does it take him to cross the river?
c) How far is his landing point downstream from his starting point?
d) How long would it take him to cross the river if there were no current?
6) a) A kayaker can paddle in still water at an average speed of 1.5 m/s. He wishes to cross a 120m wide
river and arrive at a point 20m up stream. To do so he must head his boat at an angle of 40 degrees
upstream from a point directly across the stream. What is the speed of the current?
b) Suppose the kayaker wanted to head 40m downstream and needed to head at an angle of 10 degrees
downstream of a point directly across the river, then what would the speed of be the current’s speed?
7) The pilot of a boat wishes to cross a 150m wide river. The dock where he is to land is 50m
downstream. The current is 2 m/s and his boat cruises at 12m/s in still water.
a) Calculate the time needed to cross the river.
b) What is the direction that the boat must head relative to the upstream shoreline?
c) Suppose the boat pilot wished to land at a point 50m upstream how much time would it take to cross
the river?
d) If he wished to land directly across the river then at what angle must he head relative to the
upstream shoreline?
8) A plane wishes to fly in a northwesterly direction. A steady wind from 10 degrees east of north blows
at 90 km/h. If the plane has a ground speed of 450 km/h then:
a) what is the air speed of the plane?
b) in which direction should the plane head (point)?
9) A flower pot falls from the top of an 80 m tall building. Simultaneously a ball is thrown upwards from
the bottom of the building at 75m/s. How many seconds later do they meet? Sketch a distance versus
time graph and use two equations and two unknowns.
10) A mig. 21 is approaching the U.S.S. Venus at 600m/s in level flight. When the mig is 4000m away, the
Venus fires a surface to air missile that accelerates horizontally at a constant 35m/s2 .
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a) Assuming that the mig holds its course, then at what horizontal distance from the ship is the plane
when it is intercepted by the missile?
b) If the missile is fired at an angle of 57 degrees up from the horizon then what was the altitude of the
plane?
11) Sketch a diagram of the following three forces acting on an object. A=65N at 35 degrees north of east,
B= 45N south, C=60N northwest.
Calculate:
a) The components of each vector. [watch your negative values]
b) The acceleration of a 2 kg object [remember f=ma]
c) C + B - A
d) A - B - C
12) A rock is thrown off a 300m cliff with a horizontal velocity of 40m/s.
a) Calculate the net velocity of the rock at the instant it hits the ground.
b) How far from the base of the cliff does it hit the ground?
13) An arrow is fired into the air from a height of 1.7m and with a net velocity of 95m/s. If it hits a target
at the same height and 245m away, then
a) at what angle relative to the ground does the arrow penetrate the target?
b) what is the maximum height that the arrow attained?
c) what was the net velocity of the arrow 0.35s after being released?
d) find the components of the net velocity at t=0.35s.
14) A boy traveling in the back of a truck moving at 100km/h (don’t do this at home) throws a steal ball
into the air.
a) If he catches it 4.5 s later then, what was the net velocity of the ball relative to the horizontal just
after releasing the ball?
b) At the instant the boy releases the ball the truck made a sudden stop and slowed at 2.5m/s 2 How far
ahead of the boy will the ball land? The boy released the ball at a height of 2.5m off the pavement.
c) What was the net velocity of the ball when it hit the pavement?
15) A deer wishes to jump over a 2.25m high fence.
a) If it jumps 2m ahead of the fence and jumps at an angle of 25 degrees from the zenith, then what is
the initial net velocity of the dear?
b) Why can you not use the equation for range to solve the problem in part “a”?
16) A zoologist wishes to drop a net on a deer during a population study. The plane from which the net is
dropped flies at 95km/h at an altitude of 30m at the time the net is dropped. The net experiences strong
wind and air resistance the instant it is released. Consequently, net’s horizontal acceleration is 5m/s
each second and its vertical acceleration is 8m/s each second. If the target deer runs at 43km/h then at
what distance from the deer must the net be released?
17) A plane is about to drop a parcel to a group of people on the ground. The plane is traveling at 250km/h
and at an altitude of 500m.
a) At what angle from the plane’s cockpit relative to the horizon must the group be if they are to
receive the parcel?
b) If the plane is a horizontal distance of 400m ahead of the group when it releases the parcel then at
what vertical velocity must the parcel be released with?
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