Question

Swimmer runs straight off a cliff that is 10 meters high. He must clear the rocks below to make it into the water. Water's edge is 4 meters from the edge of the cliff. What speed must the swimmer leave the cliff to make it into the water?

Answer 1

Let's first find the time that the swimmer takes to reach the water:

$$y=\dfrac{1}{2}gt^2,$$ $$t=\sqrt{\dfrac{2y}{g}}=\sqrt{\dfrac{2\cdot10\ m}{9.8\ \dfrac{m}{s^2}}}=1.43\ s.$$

Finally, we can find the speed that the swimmer must attain to leave the cliff and to make it into the water:

$$x=v_0t,$$ $$v_0=\dfrac{x}{t}=\dfrac{4\ m}{1.43\ s}=2.8\ \dfrac{m}{s}.$$