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Math Help - Free fall motion problem

  1. #1
    Member diddledabble's Avatar
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    Free fall motion problem

    I started this and then got stuck I think it is my integral that caused the problem.

    A 400 lb object is released from rest 500 ft above the ground and allowed to fall under the influence of gravity. Assuming that the force in pounds due to air resistance is -10v, where v is the velocity of the object in ft/sec, determine the equation of motion of the object. When will it hit the ground.

    v=0
    m=400
    g= 32 ft/sec^2

    F1= 400(32)=12800
    F2=-10v

    m(dv/dt)= f1+f2=12800-10v

    (dv/dt)=32-(1/40)v
    v(0)=0

    (1/32)-40vdv=-dt
    (1/32)v-20v^2=-t+c

    v(t)=1280-1280e^(-1/40)t
    v(0)=1280-1280e^(-1/40)(0)=0
    t=c

    Please explain where I went wrong.
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  2. #2
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    Quote Originally Posted by diddledabble View Post
    I started this and then got stuck I think it is my integral that caused the problem.

    A 400 lb object is released from rest 500 ft above the ground and allowed to fall under the influence of gravity. Assuming that the force in pounds due to air resistance is -10v, where v is the velocity of the object in ft/sec, determine the equation of motion of the object. When will it hit the ground.

    v=0
    m=400
    g= 32 ft/sec^2

    F1= 400(32)=12800
    F2=-10v

    m(dv/dt)= f1+f2=12800-10v

    (dv/dt)=32-(1/40)v
    v(0)=0

    (1/32)-40vdv=-dt Mr F says: This is totally wrong. Please show all the steps leading to it. Hopefully, this will cause you to see why it's very wrong. If not, it will at least be possible to point out the fundamental misunderstanding(s) you have with basic algebra.

    (1/32)v-20v^2=-t+c

    v(t)=1280-1280e^(-1/40)t
    v(0)=1280-1280e^(-1/40)(0)=0
    t=c

    Please explain where I went wrong.
    If you're studying differential equations you're expected to have a firm grasp of basic algebra.
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