Question

PLEASE HELP! I'VE BEEN STUCK FOR FOUR DAYS!!!
A movie stunt driver on a motorcycle speeds horizontally off a 50.0m high cliff. How fast (in km/h) must the motorcycle leave the cliff-top if it's to land on the level ground below at a distance of 90.0m from the base of the cliff? [Answer is 101km/h] I keep getting 1.6, I need an explanation.

Answer 1

The time it takes to fall 50 meters will be
\[ \Delta t = \sqrt{\frac{2\cdot 50 \text{m}}{9.8 \text{m}/\text{s}^2} } \approx 3.19 \text{ s}\]
The necessary horizontal speed to cover 90 m in that time is
\[ v_x = \frac{90 \text{m}}{3.19 \text{s}} = 28.2 \text { m/s }\approx 101 \text{ km/h} \]