Word Problem Math

Question

A ball is propelled upward from ground level. After T seconds, its height in feet is a function defined by f(t)=-16t^2+128t

After how many seconds will it reach a height of 112 feet.

Answer 1

Alright, Joe, we have the info we need. We just need to plug it in and solve for t. If the function gives us the height, then...

 

-16t² + 128t = 112

-16t² + 128t - 112 = 0

 

To make this easier to deal with, I'm going to divide the entire thing by -16. Remember that the function still says the same, no matter what I multiply or divide by.

 

t² - 8t + 7 = 0

(t - 1)(t - 7) = 0

 

t - 1 = 0

t = 1

 

t - 7 = 0

t = 7

 

It will take just 1 second on the way up, and 7 seconds on the way down!