Suppose a baseball is tossed up...

Question

Suppose a baseball is tossed up and it's height as a function of time is given by the formula: h= -16t^2 + 64t + 10 where "h" is the height of the baseball measured in feet and "t" is time measured in seconds.

 

1) What is the height of the baseball at 3 seconds?

2) Find the maximum height of the baseball and the time at which that height is attained.

3) When will the baseball be 60 feet in the air?

 

I'm having trouble solving these problems. Any help is greatly appreciated!

Answer 1

Hi Brianna,

 

You're given the equation h = -16t² + 64t + 10, to find the height at any time t.

 

1) What is the height of the baseball at 3 seconds?

Plug in t=3 and find the height.

 

2) Find the maximum height of the baseball and the time at which that height is attained.

The maximum height of the baseball will be at the vertex of its path. The vertex of a parabolic path is when

t = -b/2a for an equation in standard form at² + bt + c. In this case,

t = -(64)/2(-16) = -64/-32 = 2 sec

To find the height at this time, plug 2 into the equation and simplify.

 

3) When will the baseball be 60 feet in the air?

This is asking the time at which h = 60, so

60 = -16t² + 64t + 10    //subtract 60 from both sides

0 = -16t² + 64t - 50

 

To solve this you can either try factoring or use the quadratic formula. Using the quadratic formula:

 

t = [-b ± √(b² - 4ac)] / 2a

t = [-64 ± √(64² - 4(-16)(50)) ] / 2(-16)

 

Simplify and reduce as much as you can, and that will be your answer.