How long does he have until the ball reaches the ground?

Question

Draco steals and throws Neville's red ball straight up at 78 feet per second from about 10 feet above the ground. The ball's height in feet above the ground after t seconds is given by h(t)=−16t^2+78t+10.

How long does he have until the ball reaches the ground?

Answer 1

The ball reaches the ground when h(t) = 0

 

You are given h(t).  Set h(t) = 0 and solve the resulting quadratic equation for t.  The positive solution will be the time it takes for the ball to hit the ground.

Answer 2

 h(t)=−16t^2+78t+10

 

As Arturo stated, when the ball hits the ground the height will be zero feet so

 

-16t² + 78t + 10 = 0    solve for t

Note all terms are divisible by 2 so we can reduce this

-2(8t² - 39t - 5) = 0

 

8t² - 39t - 5 = 0 

 

We can use the quadratic equation to solve this

t = [-b ±√(b²-4ac)]/2a  with a=8, b=-39, c=-5

 

t = [39±√((-39)²-4(8)(-5))]/2(8)

 

From there solve for t.  Discard the negative answer.