Height equation problems

Question

A baseball is hit so that its height can be modeled by the equation

h(t)-=-4.9t^2+115t+6

where h(t) represents the height in meters of the baseball t seconds after the ball is hit.

a.) what is the starting height of the baseball?

b.) what is the maximum height of the baseball?

c.) when does the baseball reach its maximum height?

d.) when does the baseball hit the ground?

 

 

Answer 1

a)

 

Starting is when t=0.   Evaluate h(0).

 

 

c) and b)

 

Use the equation     t = -b / (2a)   --->  x-coordinate of the vertex

 

where:

a = -4.9

b = 115

 

Plug in these value into the formula to solve for t.  This will give you the time of maximum height.  Then evaluate h(t) at this value of t to find the maximum height.

 

 

d)

 

Set  h(t)=0 and solve for t.  Use the quadratic formula

 

t = (-b ± √(b² - 4ac)) / 2a

 

 

to find the x-intercepts.