Question

suppose you are going cliff diving. the top of the cliff slopes upward 10 degrees. you run up this slope as fast as you possibly can and continue off of the cliff at 10 degrees above the horizontal. 21 m below there are rocks that extend 3 m from the edge of the cliff. after that there is deep water. is it humanly possible for you to jump off an safely land in the deep water

Answer 1

consider the motion along the X-direction

V_ox = initial velocity = v Cos10

X = horizontal displacement = 3

using the equation

X = V_ox t

3 = (v Cos10) t

t = 3 /(v Cos10) eq-1

consider the motion along the Y-direction

V_oy = initial velocity = v Sin10

a = acceleration = - 9.8

Y = vertical displacement = -21

t = time of travel

using the equation

Y = V_oy t + (0.5) a t²

- 21 = v Sin10 t + (0.5) (- 9.8) t²

using eq-1

- 21 = v Sin10 (3 /(v Cos10)) + (0.5) (- 9.8) (3 /(v Cos10))²

v = 1.5 m/s

this speed can be gained by the human.