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

Answer:

$1+2\sqrt{2}$ seconds

Step-by-step 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:

$t=\dfrac{2\pm\sqrt{4+28}}{2}= \\\\\dfrac{2\pm4\sqrt{2}}{2}= \\\\1\pm2\sqrt{2}$

Since the time must be positive, it takes the ball $1+2\sqrt{2}$ seconds to hit the ground, or around 3.828. Hope this helps!