A body is thrown down from h = 35m with v = 12m/s. Find the speed when the body hits the ground if there is no air resistance and if 10% of the mechanical energy is lost.
b)10% of its mechanical energy is lost
The body is thrown down from a height of 35 m with a velocity of 12 m/s which is assumed to be in the downward direction. On a freely falling body there is an acceleration due to the gravitational force of attraction of the Earth in the downward direction. This is equal to 9.8 m/s^2.
For a body that has an initial velocity of u, travels for s meters under an acceleration a and has a final velocity v, the relation between all the variables is v^2 - u^2 = 2*a*s or v^2 = u^2 + 2*a*s.
Substituting the values given: v^2 = 12^2 + 2*9.8*35, or v = 28.8 m/s.
When there is a 10% loss in kinetic energy the final velocity v'^2 = 0.9*v^2 = 0.9*830 or v' = 27.33 m/s
The velocity of the body when it hits the ground is 28.8 m/s when there is no loss and 27.33 m/s when there is a 10% loss in kinetic energy.