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:
[tex]E_{i} = K_{i} + U_{i} = 0 + U_{i} (1)[/tex]
- 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):
[tex]m*g* h = 2*\frac{1}{2}*m*v^{2} (2)[/tex]
- Dividing both sides by m, simplifying, and solving for v, we get:
[tex]v = \sqrt{g*h} =\sqrt{9.8m/s2*4.0m} = 6.26 m/s (3)[/tex]
- v = 6.3 m/s (with two significative figures)
