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Derivative problem

  1. Feb 3, 2008 #1
    1. The problem statement, all variables and given/known data
    "If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after t seconds is given by H = 10t - 1.86t^2."

    a) Find the velocity of the rock when t = a
    b) Find the velocity of the rock after 1 second
    c) When will the rock hit the surface?
    d) With what velocity will the rock hit the surface?

    3. The attempt at a solution

    I was able to do parts a and b. Im stuck at c and d though.

    For (a) I derived the formula that is given.
    Which turns to: 10 - 3.72a
    For (b) I substituted 1 into the equation which gives: 6.28

    Now how would I go about finding out when the rock will hit the surface and it's velocity? Any help appreciated.
     
  2. jcsd
  3. Feb 3, 2008 #2
    your velocity is the derivative.... v= 10-3.72t

    there are going to be 2 times when the rock is on the ground.
    one at time zero and one at the 2nd time... which is 10/1.86t

    1.86t2-10t=0
    1.86t=10
    t=0 and t= (about) 5.37

    to find the velocity

    you plug in 5.37 into the derivative:

    v= 10-3.72t
    = 10-3.72(5.37)= -9.9764

    which equals... negative 10
    as we can see, it was thrown up at 10 m/s and coming down it should be the opposite of that... -10.

    :) enjoy!

    need any more explanations?
     
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