Unless otherwise stated, all objects are located near the Earth\'s surface, wher

Question

Unless otherwise stated, all objects are located near the Earth's surface, where g = 9.80 m/s^2 .
Jane and John, with masses of 49kg and 68kg , respectively, stand on a frictionless surface 14m apart. John pulls on a rope that connects him to Jane, giving Jane an acceleration of 0.94m/s^2toward him.

a)What is the magnitude of the John's acceleration?

b)What is the direction of the John's acceleration? away from Jane or toward Jane

c)If the pulling force is applied constantly, where will Jane and John meet?from John

Explanation / Answer

a) Force on Jane = m*a = 49*0.94

Accelaration of John = m*a/m' = 49*0.94/68 = 0.677 m/s^2

b) Direction of John's accelaration is towards Jane.

c) Since the force applied is constant, the accelaration is constant.

Let the distance be x from John.

So john travels x m and Jane travels 14-x m.

Let time taken by both = t

Final velocity of John = 0.677*t

Final Velocity of Jane = 0.94*t

For John

v^2 = u^2 + 2*a*s => 0.677*0.677*t*t = 0 + 2*0.677*x

x = 0.677*t*t/2

t*t = 2x/0.677

For Jane

v^2 = u^2 + 2*a*s => 0.94*0.94*t*t = 0 + 2*0.94*(14-x)

14-x = 0.47*t*t

14 = 0.47*2x/0.677 +x = 2.388x

x = 14/2.388 = 5.86 m from John.

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