Relative Motion Problems

1. The pilot of a light plane heads due North at an airspeed of 400 km/h. A wind is blowing from the west at 60 km/h.
   1. What is the ground velocity?
   2. How far off course would the plane be after 2.5 h, if the pilot had hoped to travel north, but had forgotten to check the wind velocity?

1. A canoeist paddles north across a river 3.0 m/s (The canoe is always kept pointing at right angles to the river). The river is flowing east at 4.0 m/s and is 100 m wide.
   1. What is the velocity of the canoe relative to the river bank?
   2. Calculate the time to cross the river
   3. How far downstream is the landing point from the starting point?

1. A pilot wishes to make a flight of 300 km[NE] in 45 min. On checking with the meteorological office, she finds that there will be a wind of 80 km/h from the north for the entire flight. What heading and airspeed must she use for the flight?

1. A quarterback is running across the field, parallel to the line of scrimmage, at a constant speed of 2.5 m/s, when he spots an open, stationary receiver straight downfield from him (i.e. in a line parallel to the sideline). If he can throw the football at a speed of 8.0 m/s, relative to himself, at what angle, relative to the sideline, must he throw it in order to hit the receiver? How far downfield was the receiver, if the pass took 3.0 s to reach him.

1. A dog walks at 1.6 m/s on the deck of a boat that is travelling at 7.6 m/s with respect to the water.
   1. What is the velocity of the dog with respect to the water if it walks towards the bow (front)?
   2. What is the velocity of the dog with respect to the water if it walks towards the stern (back)?
   3. What is the velocity of the dog with respect to the water if it walks towards the starboard (right)?

1. An airplane maintains a heading due west at an airspeed of 900 km/h. If it is flying through a hurricane with winds of 300 km/h from the northeast:
   1. In which direction is the plane moving, relative to the ground?
   2. What is the planes ground speed?
   3. How long would it take the plane to fly from one city to another, 500 km away, along the path from a.

1. Two boathouses are located on a river, 1.0 km apart on the same shore. Two men make round trips from one boathouse to the other and back. One man paddles a canoe at a velocity of 4.0 km/h relative to the water, and the other walks along the shore at a constant velocity of 4.0 km/h. The current in the river is 2.0 km/h in the starting direction of the canoeist.
   1. How much sooner than the walker does the canoeist reach the second boathouse?
   2. How long does it take each to make the round trip?

1. A 70 m wide river flows at 0.80 m/s. a girl swims across it at 1.4 m/s relative to the water.
   1. What is the least time she requires to cross the river?
   2. How far downstream will she be when she lands on the opposite shore?
   3. At what angle to the shore would she have to aim in order to land directly opposite where she started?
   4. How long would the trip from c. take?

1. An ocean liner is travelling at 18 km/h due south. A passenger, strolling on the deck, walks towards the rear of the ship at 3.0 m/s. After walking for 12 s, he turns right and walks at the same speed towards the side rail, 15 m from his turning point.
   1. What is his velocity, relative to the water while walking towards the rear?
   2. What is his velocity, relative to the water while walking towards the side rail?
   3. Draw a vector diagram and determine the overall displacement of the man.

1. A newspaper boy throws a paper sideways onto the porches of his customers while riding his bicycle along the sidewalk. The sidewalk is 15 m in front of the porches. The boy throws the papers at a horizontal speed of 6.0 m/s, relative to himself, and rides the bike at a speed of 4.0 m/s relative to the sidewalk.
   1. With what horizontal speed do the papers actually travel at?
   2. How far in advance of the porch should the paperboy throw the paper in order for the paper to land on the porch?
   3. If he waits until he is directly opposite a porch, at what horizontal angle, with respect to the sidewalk will he have to throw the paper in order for the paper to land on the porch?

1. A pilot maintains a heading due west with an airspeed of 240 km/h. After flying for 30 min he finds himself over a town that he knows is 150 km west and 40 km south of his starting position.
   1. What is the wind velocity?
   2. What heading should he now maintain, with the same air speed, to follow a course due west from the town?

1. The navigator of an airplane plans a flight from one airport to another 1200 km away in a direction 30^o east of north. The weather office informs him of a prevailing wind from the west, of 80 km/h. The pilot wants to maintain an airspeed of 300 km/h.
   1. What heading should the navigator give the pilot?
   2. How long will the flight take?
   3. How much time did the wind save?