SOLUTION: 1. At her highest point, a girl on a swing is 7ft above the ground, and at her lowest point she is 3ft above the ground. What is her maximum velocity?

Algebra ->  Test -> SOLUTION: 1. At her highest point, a girl on a swing is 7ft above the ground, and at her lowest point she is 3ft above the ground. What is her maximum velocity?      Log On


   

Question 1199641: 1. At her highest point, a girl on a swing is 7ft above the ground, and at her lowest point she is 3ft above the ground. What is her maximum velocity?
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
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At her highest point, a girl on a swing is 7ft above the ground,
and at her lowest point she is 3ft above the ground. What is her maximum velocity?
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At her highest point on the swing, velocity is zero.

Velocity is maximum at her lowest point.


Apply the conservation mechanical energy law

     %28mv%5E2%29%2F2 = mgh%5Bhighest%5D - mgh%5Blowest%5D


in standard designations.  Reduce the factor of mass m in both sides and substitute
the given values.  You will get

    v%5E2%2F2 = 32*7 - 32*3 = 128,

    v%5E2 = 2*128 = 256

    v = sqrt%28256%29 = 16.


ANSWER.  The maximum velocity is 16 ft/s at the lowest point.

Solved.

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When we solve this problem, we assume that the mass of the girl
is concentrated in one single point.

Surely, in real life it is not so - - - therefore,
this solution is only APPROXIMATE to real life.

In real life, different points of a body move with different velocities,
but we neglect (!) this fact when solving the problem.