Question

A man is crossing a river of width 100 m on a motorboat. The velocity of the motor boat is 4 m/s eastward and the velocity of the water current is 3 m/s northward.
What is the resultant velocity of the boat and how much time will it take for the man to reach the other shore of the river?

A) The resultant velocity of the motor boat is 5 m/s and it takes 20s to cross the river.

B) The resultant velocity of the motor boat is 25 m/s and it takes 5s to cross the river.

C) The resultant velocity of the motor boat is 6 m/s and it takes 20s to cross the river.

D) The resultant velocity of the motor boat is 4 m/s and it takes 33s to cross the river.

Answer 1

By the Pythagorean theorem we get $3^2+4^2=5^2$. Thus the resultant velocity will be 5 m/s.

However there is a typo in the choices. It should take 25 seconds to cross the river, not 20 seconds, since the boat actually travels 125 meters due to the water current, and 125/5 = 25 seconds.

Alternatively  you can calculate the eastward component of travel and get 100 / 4 = 25 seconds.