Question

1. (Spts) A 1-kg rock drops from a vertical cliff hat is 4 m tll anderns nogi air resistance as it falls. At what speed will its gravitational potential energy (relative to the base of the cliff) be equal to its kinetic energy?

Answer 1

From equation of motion the speed of the rock after falling a distance h is V^2 - U^2 = 2gh V^2 - 0 = 2gh V = squareroot 2gh After falling a distance +ve kinetic energy is equal to its potential energy so, we have mg(4.0m - h) - 1/2 mv^2 Substitute 2gh v^2 to slove for h mg (4.0m - n) = 1/2 m (2gh) (4m - h) = 1/2 (2h) (4m - h) = h 2h = 4m rightdoublearrow h = 2m therefore The speed of the rock is V = squareroot 2gh = squareroot 2 (9.8 m/s^2) (20 m) V = 6.3m/s