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A model rocket is launched straight upward with an initial speed of 45.0 m/s. It accelerates with a constant upward acceleration of 1.50 m/s2 until its engines stop at an altitude of 160 m.

A. what is the max height reached by the rocket?
B. How long after liftoff does the rocket reach its maximum height?
c. How long is the rocket in the air?

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  1. stage one:
    h = 45 t + (1/2)(1.5) t^2 = 160
    solve for t
    .75 t^2 + 45 t - 160 = 0
    t = 3.367 seconds
    v = 45 + 1.5 t = 45 + 1.5(3.367) = 50.05 m/s

    stage 2
    v = Vi - g t
    at top v = 0
    9.81 t = 50.05
    t = 5.1 seconds drifting up
    h = 160 + 50.05(5.1)-4.9(5.1)^2
    = 160 + 255 - 127
    = 287 meters at the top
    time so far = 3.4+5.1 = 8.5 seconds

    stage 3, ignominious fall to ground
    h = 287
    so
    287 = 4.9 t^2
    t = 7.65 second fall
    so
    time in air = 8.5 + 7.7 = 16.2 seconds

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