Question 1181908: A rocket is launched straight upwards with an initial velocity of 80 m/s. The height of the rocket, h, in metres, can be modelled by h = -5t^2 + 80t, where t is the elapsed time in seconds.
a) Sketch a graph that shows the height of the rocket versus time (Label the following y-intercept,
vertex, x-intercepts).
b) After how many seconds does the ball hit the ground?
c) What is the maximum height reached by rocket? When does it reach this height?
d) How long does it take for the rocket to reach a height of 275 m?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! f(t)=-5t^2+80
maximum height is at t=-b/2a or -80/-10 or 8 seconds.
f(8)=-320+640=320 feet.
since the graph is symmetrical around t=8 seconds,, it hits the ground in 16 seconds.
-5t^2+80t=275
-5t^2+80t-275=0
-5(t^2-16t+55)=0
(t-11)(t-5)=0
at 5 seconds. That is for the first time, which is how I interpret the question, but it also will occur at 11 seconds on the way down.
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