Quadratic Functions

Question

 The path of a rocket is given by the function, h(t)=-15t2+150t+365, where “h” is the height in metres and “t” is the time in seconds.

a) What is the maximum height of the rocket? 

b) At what time does the rocket reach its maximum height?

c) At what time does the rocket land?

d) What is the domain and range of the rocket’s function?

Answer 1

-15t^2 +150t +365

take the derivative and set equal to zero

-30t +150 = 0

t = 150/30 = 5 seconds to reach max height

h(5) = -15(5^2) +150(5) + 365 = -375 + 750 +365 = 740 feet high = maximum height

it hits the ground when h(t) =0 = -15t^2 +150t + 365

3t^2 -30t - 73 = 0

t = 30/6 + (1/6)sqr(900+12(73)) = about 12.024 seconds, slightly more than 12 seconds

It goes to max height in 5 seconds, then returns to the initial height of 365 feet in another 5 seconds, or 10 seconds total, then in another 2 seconds it reaches the ground.

domain is the values of t, 0<t< about 12.024 seconds Or in interval notation [0,12.024]

range is the values of h(t) 0<h< 740 feet or in interval notation [0, 740]

But there is a chance there is a mistake in the problem, a typo. Usually the t^2 term has a coefficient of -16 which reflects the force of gravity in feet per second per second or -4.9 if it's measured in meters

so if there's an answer key with a different answer, that may be why