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Math Help - arrow problem.

  1. #1
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    arrow problem.

    Theres An arrow, starting from rest, it leaves the bow with a speed of 24.5 m/s.

    If the average force exerted on the arrow by the bow were doubled, all else remaining the same.

    so with what speed would the arrow leave the bow?

    of course in m/s?

    please help.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rcmango View Post
    Theres An arrow, starting from rest, it leaves the bow with a speed of 24.5 m/s.

    If the average force exerted on the arrow by the bow were doubled, all else remaining the same.

    so with what speed would the arrow leave the bow?

    of course in m/s?

    please help.
    f=ma,

    so assuming constant force while accellerating:

    a=f/m

    v=(f/m)t

    s=(f/m) (t^2/2).

    So assume a 1m pull on the bow, we have the time on the bow is:

    t=sqrt(2m/f)

    and so the speed at which the arrow leaves the bow is:

    v=sqrt(2f/m).

    Hence doubling the force increases the speed by a factor of sqrt(2).

    Alternativly, work done = change in KE = force*distance.

    Hence doubling the force doubles the KE, but KE is proportional to the
    square of speed, so speed incread=ses by a factor of sqrt(2).

    RonL
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