Question

A few people push a boat in order to make it move as fast as possible before they get in. Taking into consideration that these people apply an avg. force of 150 N in the direction of motion of the 90 kilogram boat for 7 seconds, what will be the boat's speed at that point? (Don't take friction into consideration).

Answer 1

Use conservation of energy. On the left, we have an expression for work transferred to the boat, and on the right we have an expression for final kinetic energy. Here, force is \(\vec F\), displacement is \(\vec r\), mass of boat is \(m\), and final velocity of boat is \(v_f\).
\[\underbrace{\int \vec F \cdot d\vec r}_{\text{Work}}=\underbrace{\frac 12 mv_f^2}_{\text{Kinetic}}\]Since the force is always constant and also always in the direction of the displacement, we can drop the integral as well as the dot product and vector notation.\[F \Delta r = \frac{1}{2}mv_f^2\]We can now solve for velocity.\[\boxed{\displaystyle v_f = \sqrt{\frac{2F\Delta r}{m}}}\]Plug in given values and evaluate on a calculator to get your answer.