# Some problems involving relative motion

A river flows to the South at 3 km/hour. The city of Townsville sits on the river's bank. Joe's house is 15 km North of the city, also on the river's bank. Joe can paddle his kayak so that he moves at a speed 5 km/hour relative to the water.

1. Joe leaves his house and paddles towards Townsville. What is his velocity relative to a person standing on the bank of the river?
2. How long does it take Joe to travel from his house to Townsville?
3. How long does it take Joe to travel from Townsville back to his house?

At the location of Joe's house, the river is W = 600 m wide. Joe's girlfriend, Anne, lives in a house which is on the East bank of the river, directly across the river from Joe's house.

Joe wants to paddle his kayak so that he will travel in a straight line to Anne's house. He discovers that if he points his kayak straight to the East, he ends up far below Anne's house when he reaches the East bank.

1. In what direction should Joe point his kayak so that it does travel due East to Anne's house?
2. How long does it take Joe to cross the river in this way, going from his house to Anne's house?
3. How long does it take Joe to go back to his own house?