Question

During an experiment, a ball is dropped from a height of 205 feet. The formula h = -16t2 + h subscript 0 can be used to approximate the number of seconds t it takes for the ball to reach height h from an initial height of h subscript 0 in feet. Find the time it takes the ball to reach the ground.

Answer 1

Answer:

4 seconds

Step-by-step explanation:

$h = -16t^2 + h_0$

where h=height reached after t seconds

         $h_0$ = Initial Height of the ball

The ball is dropped from a height of 205 feet,

$h_0$ = 205 feet

We want to determine the time it takes the ball to reach the ground.

i.e. when height of the ball, h=0

Substituting $h_0$ = 205 feet and h=0 into the formula

$h = -16t^2 + h_0$

$0 = -16t^2 + 205$

Add $16t^2$ to both sides

$0+16t^2 = -16t^2+16t^2 + 205\\16t^2=205$

Divide both sides by 16

$\frac{16t^2}{16}= \frac{205}{16}\\t^2=12.8125$

$t=\sqrt{12.8125} =3.58$ ≈ 4 Seconds

It takes approximately 4 seconds for the ball to reach the ground.