A model rocket is launched from the deck in Raven's backyard and the path followed by the rocket can be modeled by the relation h=-5t^2 + 100t + 15

Question

A model rocket is launched from the deck in Raven's backyard and the path followed by the rocket can be modeled by the relation h=-5t^2 + 100t + 15, where h, in meter, is the height that the model rocket reaches after t seconds. 

a) what is the maximum height reached by the model rocket? 

b) What is the height of the deck?

c) When us the rocket at a height of 200 m, to the nearest second?

Answer 1

take the derivative and set it equal to zero

-10t +100 =0

10t =100

t = 10 seconds at max height

-5(10)^2 +100(10) + 15 = 515 max height

deck = 15

h= 200 = -5t^2 +100t +15

-5t^2 +100t -185 =0

t^2 - 20t + 37 =0

t + 20/2 + or - (1/2)sqr(400-148) = 10+ or - .5(sqr(252) = 10 + or 7.9 = 17.9 or 2.1 seconds