High School

A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 80 feet per second. The height h, in feet, of the rocket above the ground at t seconds

after launch is given by the function h(t) = - 16 + 80t + 7. How long will it take the rocket to reach its maximum height? What is the maximum height?

A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 80 feet

Answer :

It will take the toy rocket 2.5 seconds to reach its maximum height.

The maximum height is 107 feet.

How long will it take the rocket to reach its maximum height?

For a quadratic function of the form h(t) = at² + bt + c

where a, b and c are constants

The maximum of value of t is:

tmax = -b/2a

In this case, we have:

h(t) = -16t² + 80t + 7

Thus,

a = -16, b = 80 and c = 7

tmax = -b/2a

tmax = -80 / (2*(-16))

tmax = -80/(-32)

tmax = 2.5 seconds

Thus it will take the toy rocket 2.5 seconds to reach its maximum height

To find the maximum height, subtitute tmax = 2.5 seconds into h(t) = -16t² + 80t + 7. That is:

h(t) = -16t² + 80t + 7

h(2.5) = -16(2.5)² + 80(2.5) + 7

h(2.5) = -100 + 200 + 7

h(2.5) = 107 feet

Thus, the maximum height is 107 feet

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