A river 100 m wide flows 1 m/s due south. A boat that travels 1 m/s relative to the water is pointed due east as it crosses from the west bank. Relative to its starting point, the boat travels
A)nowhere.
B)100 m.
C)141 m.
D)200 m.
E)more than 200 m.

Question

Quizplus · Accepted Answer

Since the boat is pointed due east, it is perpendicular to the direction of the river flow. This means the boat's velocity relative to the ground will form a right-angled triangle with the velocity of the river. The distance traveled by the boat relative to its starting point can be found using the Pythagorean theorem:

distance = √((velocity of boat relative to ground)^2 + (velocity of river)^2) * time

distance = √((1 m/s)^2 + (1 m/s)^2) * (100 m / 1 m/s)

distance = 141.4 m or approximately 141 m

Therefore, the boat travels 141 m relative to its starting point.

A River 100 M Wide Flows 1 M/s Due South