1. Suppose you held a ball at a height h above the ground and thendropped it. a.

Question

1. Suppose you held a ball at a height h above the ground and thendropped it.
    a. What is the expression for the total energyof the ball at a height h just before you drop it

    b. What is the expression for the total energyof the ball just before the ball hits the ground
    (height = 0, velocity = vf)?

    c. Use the Conservation of Mechanical Energy andthe expressions found in (a) and (b) to write
    a single energy equation for the ball as itfalls from a height of h to a height of 0

    d. Solve the expression in (c) for the finalvelocity vf. Write it in terms of the variables m, g and h.

It would be great if someone could help me out! Thank you!

Explanation / Answer

(a)    Total energy at a height 'h' = potentialenergy at height 'h'                                            =m g h (b)    Total energy of the ball just before theball hits the ground = kinetic energy                                                                                           = ( 1/2 ) m (Vf)2              ( where Vf = final velocity ) (c)    From law of conservation of energy, it isclear that the total energy at any point along the path remainssame                         hence total energy at any point along it's path = mgh = (1/2)m (Vf)2 (d) mgh = (1/2) m (Vf)2            Vf = ( 2g h )    

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