Question

A ball is thrown into the air from an apartment balcony and falls to the ground. The height of the ball, h metres, t seconds after being thrown is given by the formula: h=−5t2+10t+35

How long does it take for the ball to hit the ground

Answer 1

`1+2√(2)` seconds

Explanation:

When the ball hits the ground, its height will obviously be 0. Therefore, you can set up the equation the following way:

`0=-5t^2+10t+35 \\\\-5(t^2-2t-7)=0`

Plugging this into the quadratic equation, you get:

`t=(2\pm√(4+28))/(2)= \\\\(2\pm4√(2))/(2)= \\\\1\pm2√(2)`

Since the time must be positive, it takes the ball
`1+2√(2)` seconds to hit the ground, or around 3.828. Hope this helps!