# Math

A model rocket is launched straight upward with initial velocity of 22 m/s. The height of the rocket, h, in metres, can be modelled by h(t) = -5t^2 + 22t, where t is elapsed time in seconds. What is the maximum height the rocket reaches?

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1. Easy if you know calculus.

h ' (t) = -10t + 22 = 0 for a max/min of h(t)
10t = 22
t = 2.2

h(2.2) = -5(2.2)^2 + 22(2.2) = appr 24.2 m

If you don't know Calculus, the x of the vertex of your parabola is -b/(2a)
= -22/-10 = 2.2
sub in 2.2 into h(t) , same as above

If you don't know about the -b/(2a) stuff, you will have to complete the square to find the vertex.

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posted by Reiny

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