Question

A ball is thrown from the top row of seats in a stadium. The function h(t) = –16t2 + 16t + 96 gives the height, h, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?

Answer 1

Answer:

  3 seconds

Step-by-step explanation:

We assume the ground is where h=0, so the equation we need to solve is ...

  0 = -16t^2 +16t +96

Dividing by -16 gives ...

  0 = t^2 -t -6

Factoring, we get ...

  0 = (t -3)(t +2)

This has solutions t=3 and t=-2. Since we know the ball won't land 2 seconds before it is thrown, the solution is ...

  It will be 3 seconds before the ball hits the ground.

Answer 2

The ball will hit the floor after 3 seconds.

The given equation is,

Height,

• $h(t) = -16t^2+16t+96$

By dividing the above equation by "16", we get

→   $-\frac{16t^2}{16}+\frac{16t}{16}+\frac{96}{16} =0$

→              $t^2-t-6=0$  

By factorizing, we get

→     $t^2+2t-3t-6=0$

→ $t(t+2)-3(t+2)=0$  

→         $(t+2)(t-3)=0$  

→                      $t+2=0$

                             $t=-2$

→                      $t-3=0$

                             $t =3$

Time can't be negative. Thus the above answer i.e., 3 is correct.

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