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Math Help - Related Rates

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    Related Rates

    Hi, I'm having a lot of trouble with this problem. Help would be greatly appreciated

    The kinetic energy of amoving object equals half the product of itsmass and the square of its velocity. K = mV^2 As a spaceship is fired into orbit, all three ofthese quantities vary. Suppose that the kineticenergy of a particular spaceship is increasingat a constant rate of 100,000 units per secondand that mass is decreasing at 20 kg/s becauseits rockets are consuming fuel. At what rate isthe spaceship’s velocity changing when itsmass is 5000 kg and it is traveling at 10 km/s?
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    Quote Originally Posted by legolewinsky View Post
    Hi, I'm having a lot of trouble with this problem. Help would be greatly appreciated

    The kinetic energy of amoving object equals half the product of itsmass and the square of its velocity. K = (1/2)mV^2 As a spaceship is fired into orbit, all three ofthese quantities vary. Suppose that the kineticenergy of a particular spaceship is increasingat a constant rate of 100,000 units per secondand that mass is decreasing at 20 kg/s becauseits rockets are consuming fuel. At what rate isthe spaceship’s velocity changing when itsmass is 5000 kg and it is traveling at 10 km/s?
    K = \frac{1}{2}mv^2

    you are given \frac{dK}{dt} = 10^5 u/s

    \frac{dm}{dt} = -20 kg/s

    you are asked to find \frac{dv}{dt} when m = 5000 kg and v = 10 km/s

    take the time derivative of K (note that you will have to use the product rule since m and v both vary with time).

    sub in your given values and solve for \frac{dv}{dt}
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