Unit 3: Motion in Two Dimensions
Problem Set B
The following selection of problems are sample problems. Individual student problem sets will vary since numerical information is randomly-generated.
For the following problems:
A river flows due east at 2.4 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 7.2 m/s due north relative to shore. What is the magnitude of the velocity of the boat (in m/s) relative to the shore?
(Referring to the previous problem.) If the river is 239 m wide and the boat heads directly across it, then how much time (in seconds) does it take the boat to reach the opposite shore?
(Referring to the previous problem.) If the river is 239 m wide and the boat heads directly across it, then how far downstream (in meters) has the boat moved by the time it reaches the North shore?
A boat heads due east directly across a 116-m wide river. The water flows due south with a speed of 2.1 m/s with respect to the shore. The boat speed with respect to the water is 2.8 m/s. Determine the magnitude of the velocity (in m/s) with respect to the shore.
(Referring to the previous problem.) Determine the direction (in degrees) of the velocity with respect to the shore. Use the counter-clockwise from east convention.
(Referring to the previous problem.) Determine the distance (in m) that the boat will have traveled downstream when it has reached the opposite shore.
The pilot of an aircraft (flying at some angle) wishes to fly due west in a wind blowing at 44 km/h toward the south. If the speed of the aircraft in the absence of wind is 163 km/h, in what direction (in degrees) should the aircraft head? Use the counter-clockwise from east convention.
(Referring to the previous problem.) What will be the airplane's speed (in km/h) relative to the ground?
A boat travels east across a 33 m wide river in 1 seconds. If the river flows .9 m/s north, how far upstream does the boat end up?
A boat moves at 4.5 m/s relative to the water regardless of which direction it travels through the water. If the water in a river is flowing at 1.5 m/s, how long (in seconds) does it take the boat to make a trip across the river if a 284 m displacement downstream is experienced.
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