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Math Help - Differential Equations(Related Rates)

  1. #1
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    Differential Equations(Related Rates)

    I am stuck on this question, here it is.

    A ball with mass m kg is thrown upward with initial velocity 28m/sec from the roof of a building 11m high. Neglect air resistance.
    (a) Find the maximum height above the ground that the ball reaches.
    (b) Assuming that the ball misses the building on the way down find the time that it hits the ground.

    I found the answer to part (a) as 51 meters but I can't get part (b). Thanks for any help!
    Last edited by Oblivionwarrior; September 26th 2008 at 05:22 PM.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Oblivionwarrior View Post
    I am stuck on this question, here it is.

    A ball with mass kg is thrown upward with initial velocity m/sec from the roof of a building m high. Neglect air resistance.
    (a) Find the maximum height above the ground that the ball reaches.
    (b) Assuming that the ball misses the building on the way down find the time that it hits the ground.

    I found the answer to part (a) as 51 meters but I can't get part (b). Thanks for any help!
    I don't see the numerical value for speed and for height. Is the mass assumed to be some value m??

    --Chris
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    I don't see the numerical value for speed and for height. Is the mass assumed to be some value m??

    --Chris

    Thanks! fixed.
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  4. #4
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    h(t) = 11 + 28t - 4.9t^2

    part (b) ... set h(t) = 0 and solve for t.
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Oblivionwarrior View Post
    I am stuck on this question, here it is.

    A ball with mass m kg is thrown upward with initial velocity 28m/sec from the roof of a building 11m high. Neglect air resistance.
    (a) Find the maximum height above the ground that the ball reaches.
    (b) Assuming that the ball misses the building on the way down find the time that it hits the ground.

    I found the answer to part (a) as 51 meters but I can't get part (b). Thanks for any help!
    I broke up part (b) into 2 parts:

    from 11 m to 51 m (from top of building to highest point):

    Using y_f=y_0+v_0t-\tfrac{1}{2}gt^2, we see that 51=11+28t-4.9t^2\implies 4.9t^2-28t+40=0

    I'll let you solve this and show that t\approx 2.86~s

    from 51 m to 0 m (from highest point to the ground):

    Using y_f=y_0+v_0t-\tfrac{1}{2}gt^2, we see that 0=51-4.9t^2\implies 4.9t^2=51\implies t^2=10.41\implies t\approx 3.23~s

    Thus the total time for it to reach the ground, once it was thrown off the building is t=2.86~s+3.23~s=\color{red}\boxed{6.09~s}

    Does this make sense?

    --Chris
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by skeeter View Post
    h(t) = 11 + 28t - 4.9t^2

    part (b) ... set h(t) = 0 and solve for t.
    haha...wow...I can't believe I didn't think of that... >.<

    --Chris
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