Projectile and Relative Motion Review
Questions:
1) A little league baseball player and a major league baseball player each hit a fly ball to
center field. Once in flight, which ball, if either. Has the greater acceleration? Explain.
2) A wrench is accidentally dropped from the top of the mast on a sailboat. Will the
wrench hit at the same place on the deck whether the sailboat is at rest or moving with a
constant velocity? Explain.
3) A rifle, at height H above the ground, fires a bullet parallel to the ground. At the same
instant and at the same height, a second bullet is dropped from rest. In the absence of air
resistance, which bullet strikes the ground first? Explain.
4) It is true that complementary angles give equal ranges for a type II projectile, but how
do the hang times compare?
5) What factors affect the amount of time a horizontally launched projectile spends in the
air? Think about what you would use to CALCULATE the time of a horizontally
launched projectile.
6) Suppose you are bicycling on a windy day. When you ride against the wind, the wind
feels much stronger than when you ride with the wind. Why? Is there any velocity at
which you could ride your bike and would not notice the effect of the wind? If so,
explain.
7) Three swimmers can swim equally fast relative to the water. They have a race to see
who can swim across a river in the least amount of time. Swimmer A swims
perpendicular to the current and lands on the far shore downstream because the current
has swept him in that direction. Swimmer B swims upstream at an angle to the current
and lands on the far shore directly opposite the starting point. Swimmer C swims
downstream at an angle to the current in an attempt to take advantage of the current.
Who crosses the river in the least time? Explain.
Problems:
1) What is the smallest muzzle speed that a bullet can have if a horizontally fired bullet is to hit a
0.0254 m diameter target located 26.2 m away? Assume that the center of the target is on the
same horizontal line as is the barrel of the rifle.
2) A diver runs horizontally with a speed of 1.2 m/s off a platform that is 10 m above the water.
What is his speed just before striking the water?
3) A box of .22 caliber bullets has the following message written on it: “Warning! Maximum
range, 2.0 km.” Assume that the muzzle speed of a bullet is 340 m/s and calculate the maximum
range (45 degrees). Assume also that the bullet starts and ends at the same height. Give reasons
why the actual range of 2 km is less than the range you calculated.
4) A girl runs at a speed of 3.9 m/s off a high dive and hits the water 1.8 s later.
a) How high was the diving board?
b) How far horizontally was she from the board when she hit the water?
c) How long would it have taken her to hit the water if she had simply stepped off the board with
no significant horizontal velocity: less time, more time, or the same amount of time?
5) A rock is thrown horizontally from a building at 15 m/s. It hits the ground 45 m from the base
of the building. How high was this building?
6) A football is kicked from ground level at a speed of 20 m/s at 42 degrees above horizontal.
a) How long does it take to hit the ground?
b) What is the range?
7) The crossbar of a football goalpost is 3.5 m above the ground. A field goal kicker kicks a
football with a speed of 20 m/s toward the goalpost at an angle of 37 degrees above horizontal. If
the goalpost is 32 m away, is the attempt good?
8) In track and field a shot putter puts the shot with a velocity of 10 m/s at 37 degrees above
horizontal. The height of release was 2 m above the ground. The mass of the shot at the high
school level is 7.27 kg. Find the distance traveled by the shot in this effort.
9) At airports there are people movers to help people get from one place to another. A particular
people mover has a length of 105 m and is moving at a speed of 2 m/s relative to the ground. In
addition, suppose you can cover this distance (105 m) in 75 s when walking on the ground. If
you walk on the people mover at the same rate with respect to the people mover that you walk
with respect to the ground, a) How fast will you be going with respect to the ground? and, b) How
long will it take you to travel the 105 m?
10) Two cars are approaching each other in adjacent lanes. Initially the cars are 1200 m apart.
Each car has a speed of 25 m/s relative to the ground. What is the speed of each car relative to
the other car?
11) A swimmer, capable of swimming at a speed of 1.4 m/s in still water (i.e., the swimmer can
swim with a speed of 1.4 m/s relative to the water), starts to swim directly across a 200m wide
river. However, the current is 0.91 m/s, and it carries the swimmer downstream.
a) How long does it take the swimmer to cross the river?
b) How far downstream will the swimmer be upon reaching the other side of the river?