Question

a mouse is crawling inside a cart being pushed across the deck of a moving boat. The mouse is moving at 0.5km/h [E] relative to the cart. the cart is travelling at 1.2m/s[ E] relative to the deck of the boat, and the boat is moving at 4.0m/s[N] relative to the water. What is the velocity of the mouse relative to the water?

Answer 1

Speed of the mouse and cart relative to the boat:

$$v=0.5+1.2=1.7\text{ m/s}.$$

Now the boat moves at 90° relative to water. Imagine you are floating in the water looking to W sitting in E anchored to the bottom of the sea. The boat passes you from left to right at 4 m/s, the mouse in the moving cart crawls toward you. The mouse moves at some angle toward you, right? Its speed relative to water (or you) will be

$$u=\sqrt{v^2+v_\text{boat}^2}=\sqrt{1.7^2+4^2}=4.3\text{ m/s}.$$