Answer to Question #180432 in Mechanics | Relativity for Obedience

Question

A swimmer wishes to take a horizontal running start when jumping of a cliff of height h m. At the bottom of the cliff there is an exposed reef of width w m. At what speed v0 must the swimmer be running when leaving the top of the cliff, if she is to just miss hitting the reef at the bottom to enter the water? Your answer will be some expression in h, w and g = 9.8 m/s2.

Answer 1

Time taken by the swimmer to cover vertical distance $h,t =\sqrt{\dfrac{wh}{g}}$

Minimum spedd of the swimmer to miss the ledge $v_o=\dfrac{\text{ width }}{\text{ time taken }}=\dfrac{w\sqrt{g}}{\sqrt{2h}}$