Question

A ball is thrown from a height of 45 meters with an initial downward velocity of 10 m/s. The ball's height h (in meters) after t seconds is given by the following. h=45-10 t- 5 t^2. How long after the ball is thrown does it hit the ground?

Answer 1

2.16 s

Explanation:

When it hits the ground, height h=0 hence

`0=45-10t-5t^(2)`

`5t^(2)+10t-45=0`

`t^(2)+2t-9=0`

Using quadratic formula

`x=-1+\sqrt 10\\ x=-1-\sqrt 10`

Since time can't be negative,
`-1+\sqrt 10`

t=2.16 s