A small child gives a plastic frog a big push at the bottom of a slippery 2.0 meter long, 1.0 meter high ramp, starting it with a speed of 5.0 m/s. What is the frog's speed as it flies off the top of the ramp?
Because the ramp is slippery, ignore dynamic friction. Let m = the mass of the frog. g = 9.8 m/s²
The KE (kinetic energy) at the bottom of the ramp is KE₁ = (1/2)*(m kg)*(5 m/s)² = 12.5 m J
Let v = the velocity at the top of the ramp. The KE at the top of the ramp is KE₂ = (1/2)*m*v²= 0.5 mv² J The PE (potential energy) at the top of the ramp relative to the bottom is PE₂ = (m kg)*(9.8 m/s²)*(1 m) = 9.8m J
Conservation of energy requires that KE₁ = KE₂ + PE₂ 12.5m = 0.5mv² + 9.8m 0.5v² = 2.7 v = 2.324 m/s
