Answer to Question #264330 in Physics for Lhen

Question

A cliff is 22 meters high.You fell in the water 5 meters away from the hil.What is your initial horizontal velocity

Answer 1

The time $t$ of free fall (assuming no initial vertical velocity) can be found from kinematic equation:

$$h = \dfrac{gt^2}{2}\\ t = \sqrt{\dfrac{2h}{g}}$$

where $h = 22m$ is the height of the cliff, and $g = 9.8m/s^2$ is the gravitational acceleration.

Since the horizontal velocity does not changes, its initial value is:

$$v = \dfrac{d}{t} = d\sqrt{\dfrac{g}{2h}}$$

where $d = 5m$ is the horizontal range. Thus, obtain:

$$v = d\sqrt{\dfrac{g}{2h}} =5m\cdot \sqrt{\dfrac{9.8m/s^2}{2\cdot 22m}} \approx 2.4m/s$$

Answer. 2.4 m/s.