Question

A riverboat travels with a velocity of 4.60 m/s from one shore to another. The velocity of the river is 2.30 m/s. If the width of the river is 72.0 m, how far does the boat travel downstream to reach the other shore?

a) 144.0 m
b) 216.0 m
c) 288.0 m
d) 360.0 m

Answer 1

The boat travels approximately 47.93 m downstream to reach the other shore.

Step-by-step explanation:

To find the distance the boat travels downstream to reach the other shore, we need to determine the time it takes for the boat to cross the river. The time can be found by dividing the width of the river by the relative velocity of the boat and the river. In this case, the relative velocity is the sum of the boat's velocity and the river's velocity.

Time = Width / Relative Velocity
Time = 72.0 m / (4.60 m/s + 2.30 m/s) = 72.0 m / 6.90 m/s = 10.43 s

Since distance = velocity x time, the distance the boat travels downstream is:
Distance = 4.60 m/s x 10.43 s = 47.93 m

Therefore, the boat travels approximately 47.93 m downstream to reach the other shore.