Question

A person kicks a ball off of a 50m high cliff with a speed of 10 m/s. How long will it take the ball to hit the ground? * 7 points 2.3 sec 6.3 sec 4.5 sec 3.2 sec

Answer 1

Presumably, the ball is kicked parallel to the ground below the cliff, so its altitude y at time t is

`y(t)=50\,\mathrm m-\frac12gt^2`

where g = 9.80 m/s^2 is the acceleration due to gravity.

The ball hits the ground when y = 0:

`0 = 50\,\mathrm m-\frac12gt^2`

`t^2=\frac{100\,\mathrm m}g`

`t=(10)/(9.80)\,\mathrm s\approx\boxed{3.2\,\mathrm s}`