Question

The CHS baseball team wasn’t on the field and the batter popped the ball up.The equation b(t)= 80t-16t^2+3.5 represents the height of the ball above the ground in feet as a function of time in seconds. How long will the catcher have to get in position to catch the ball before it hits the ground? Round to the nearest second

Answer 1

The answer to this question is 5 seconds.

Answer 2

The given function is

`b(t) = 80t-16t^2+3.5`

Rearranging it we get

`b(t) = -16t^2+80t+3.5`

Now when the ball hits the ground

Height b(t) becomes 0.

So we have

`-16t^2+80t+3.5=0`

Comparing with

`ax^2+bx+c`

We get

a=-16, b=80 & c = 3.5

Substituting in the quadratic formula we get

`t=(-b+√(b^2-4ac))/(2a) or t=(-b-√(b^2-4ac))/(2a) </p><p>`
`t=(-80+√(80^2-4(-16)(3.5)))/(2(-16)) =-0.04`

OR

`t=(-80-√(80^2-4(-16)(3.5)))/(2(-16)) =5.04`

But the time cannot be negative

So t = 5.04 seconds

Rounding to the nearest second we get

t = 5 seconds