Question

You have a small boat which travels through water at a speed of 6.0 m/s. You take it out on a section of a local river where the water flows from north to south at a speed of 4.0 m/s.

(a) First, you head south (i.e. downstream) in your boat. Draw a vector which represents the velocity of the boat relative to the water, and a vector that represents the velocity of the water relative to the shore. Then add them and draw the vector which represents the boat’s velocity relative to the shore, and indicate its magnitude—i.e., the boat’s speed relative to the land.

(b) Now you aim your boat due east, still moving through the water at 6.0 m/s. Once again, draw vectors to show the velocity of the boat relative to the water, the velocity of the water relative to the shore, and the velocity of the boat relative to the shore. What is the boat’s speed and direction relative to the land now? (Indicate an exact direction, i.e. a number of degrees measured from some reference direction like the north.)

(c) Finally, you aim your boat due northeast, 45 degrees away from the north, still moving through the water at 6.0 m/s. Once again, draw vectors to show the velocity of the boat relative to the water, the velocity of the water relative to the shore, and the velocity of the boat relative to the shore. What is the boat’s speed and direction relative to the land now? (Indicate an exact direction, i.e. a number of degrees measured from some reference direction like the north.)

Answer 1