Carter and his girlfriend both swim at 4.0 m/s. They jump into a river 1.0 Km across, with a current of 3.0 m/s [E]

Question

a) Carter faces (heads) due north at all times. What is his velocity relative to the ground?

b) Carter's girlfriend swims straight across relative to the shore ( she does this by heading upstream a little bit) what is her velocity relative to the ground?

If anyone can solve these and explain how it's done it would greatly be appreciated.

Answer 1

a) His total velocity is the v of the boat combined with the v of the current. Since they are at right angles we can add the vectors using Pythagorean theorem v = sqrt( 3² + 4²) = 5 m/s

b) His girlfriend has to aim her swimming vector (the hypotenuse) so that the E/W component cancels the current which is 3 m/s (one of the legs of the triangle). Her N/S velocity will be sqrt(4² - 3²) = v