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azamat
3 years ago
15

A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls. At what speed w

ill it's gravitational potential energy (relative to the base of the cliff) be equal to its kinetic energy in m/s?
Physics
1 answer:
Zinaida [17]3 years ago
8 0

Answer:

v = 6.3 m/s

Explanation:

  • Since no significant air resistance exists, total mechanical energy must be kept constant at any time.
  • At the top of the cliff, all the energy is gravitational potential energy, as follows:

       E_{i}  = K_{i} + U_{i} = 0 + U_{i}  (1)

  • If we choose the ground level as our zero reference level for the gravitational potential energy, Ui is simply:
  • Ui = m*g*h (1)
  • At any height, the sum of the kinetic and the gravitational potential energy must be equal to (1).
  • We know from the question, that at the point of interest, both types of energies must be equal each other, so we can write the following expression from (1):

       m*g* h = 2*\frac{1}{2}*m*v^{2}  (2)

  • Dividing both sides by m, simplifying, and solving for v, we get:

       v = \sqrt{g*h} =\sqrt{9.8m/s2*4.0m} = 6.26 m/s (3)

  • v = 6.3 m/s (with two significative figures)
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