Calc

If a rock is thrown upward on the planet Mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H = 17t − 1.86t^2.

(a) Find the velocity of the rock after one second.
(b) Find the velocity of the rock when t = a.
(c) When will the rock hit the surface? (Round your answer to one decimal place.)
(d) With what velocity will the rock hit the surface?

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  1. As on earth, v = Vo - at where a = 1.86*2 on Mars.

    So, v = 17 - 3.72t

    v(1) = 17-3.72 = 13.28m/s
    v(a) = 17 - 3.72a

    Since h = t(17-1.86t)

    h=0 when t = 0 (rock thrown)
    and t = 9.14 (rock hits again)

    The rock will hit the surface with the same speed it had when it left: 17m/s. However, as a velocity, it's falling, so v = -17m/s

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