Question

A ball is thrown upward from a height of 15ft with an initial upward velocity of 5ft/s. Use the formula h=-16t2(t Is squared)+ vt + s to find how long it will take for the ball to hit the ground .

Answer 1

Answer:

The ball has hit the ground in about 1.137 seconds.

Step-by-step explanation:

The ball has hit the ground when the height between the ball and the ground is 0. So we will be setting h equal to 0 and then solving this equation for t.

h=-16t^2+vt+s

v represents the initial velocity

s represents the initial height

v is given as 5ft/s.

s is given as 15ft.

Inputting these in result in:

h=-16t^2+5t+15

Now we are finding for what t's do we have h=0:

0=-16t^2+5t+15

Let's calculate the discriminant to predict how messy are answers are going to be.

Discriminant=b^2-4ac

Discriminant=(5)^2-4(-16)(15)

Discriminant=25+960

Discriminant=985

It isn't a perfect square so we can't factor this.

I'm going to use the quadratic formula:

$t=\frac{-b \pm \sqrt{\text{Discriminant}}}{2a}$

$t=\frac{-5 \pm \sqrt{985}}{2(-16)}$

$t=\frac{-5 \pm \sqrt{985}}{-32}$

This implies we have two values for t to look at when h=0:

$t=\frac{-5+\sqrt{985}}{-32}$ or $t=\frac{-5-\sqrt{985}}{-32}$

Inputting both of these into the calculator:

$t=-0.824522$ or $t=1.137022$

So the answer that makes sense here is the later answer.

The ball has hit the ground in about 1.137 seconds.