Problema Solution
Alexander decided to launch one of the rockets he bought in
Acapulco. His rocket is launched vertically upward from ground level
with an initial velocity of 128 ft/s, then its height h after t seconds is
given by the equation h(t) = -16t2 + 128t (if air resistance is neglected).
a. How long will it take to for the rocket to return to the ground?
b. After how many seconds will the rocket be 112 ft above the ground?
c. How long will it take the rocket to hit its maximum height?
d. What is the maximum height?
e. Sketch a graph of the trajectory of the rocket.
Answer provided by our tutors
h(t) = -16t^2 + 128t
a. The rocket hits the ground when h(t) = 0 for some t >0, that is, we need to solve:
-16t^2 + 128t = 0
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click here to see the equation solved for t
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t = 8 s
Th rocket will return to the ground in 8 seconds.
b. We need to solve for t when h(t) = 112, that is:
-16t^2 + 128t = 112
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click here to see the equation solved for t
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t1 = 1 s
t2 = 7 s
The rocket will be 112 seconds above the ground for the first time after 1 second, for the second time after 7 seconds.
c. t = -b/2a, where a = -16, b = 128
t = -128/(2*(-16))
t = 4 s
The rocket needs 4 second to reach maximum height.
d. h(4) = - 16*4^2 + 128*4
h(4) = 256 m
The maximum height is 256 meters.