Height Function

Question

The height in feet h above the earth for sky divers t seconds after jumping from an airplane flying at a height of 6400 feet above the ground is approximated by the formula:
h(t)=-16t²+6400
subject to the constraint t < 5
Rewrite the formula with the right-hand side factored completely.
Use the result of rewriting the formula to find h(2).
Show your work; discuss your reasoning.

Answer 1

h(t)=-16t²+6400

 

h(t) = -16(t² - 400)

 

h(t) = =16(t² - 20²)

 

We have a difference of 2 squares...

t² - 20² = (t+20)(t - 20)

 

h(t) = -16(t+20)(t-20)

 

h(2) = -16(2+20)(2-20)

       = -16(22)(-18)

       =  6,336 ft

 

Two seconds after jumping out of the plane the skydiver

will be at a height of 6,336 feet above the ground.