A river 100 m wide flows due south at 1 m/s.A boat that goes 1 m/s relative to the water is pointed due east as it crosses from the west bank.The boat reaches the east bank
A)due east of where it started.
B)141 m farther south than where it started.
C)100 m farther south than where it started.
D)100 m farther north than where it started.

Question

Quizplus · Accepted Answer

Since the boat is going due east, it is going perpendicular to the direction of the river flow. Therefore, the boat's velocity relative to the ground is the vector sum of its velocity relative to the water and the river's velocity relative to the ground. Using the Pythagorean theorem, we can find the magnitude of the boat's velocity relative to the ground:
sqrt((1 m/s)^2 + (1 m/s)^2) = sqrt(2) m/s
Since the boat is only traveling east and not south, we can ignore the southward velocity of the river. Therefore, the boat travels 1 m/s east relative to the ground, which means it travels 100 m in 100 seconds. During this time, the boat also experiences a southward motion due to the river's flow. In 100 seconds, the boat would have been carried 100 m south by the river's flow. Therefore, the boat arrives at a point that is 100 m farther south than where it started.

A River 100 M Wide Flows Due South at 1