An apple falls out of a tree fro, a height of 2.3m. What is the impact speed of the apple

Answer: 6.71 m/s

Explanation:

You can use either the energy conservation law (mechanical energy conservation principle) or the kinematic equations.

Let's see:

1) kinematic equations for free fall.

Vf² = Vo² + 2gy

Where Vo = 0 which implies Vf² = 2gy.

g is 9.38 m/s²

y = 2.3 m

∴ Vf² = 2 * 9.8 m/s² * 2.3m = 45.08 m² / s²

=> Vf = √ (45.08 m² / s²) = 6.71 m/s

2) mechanical energy conservation principle

a) Change in kinetic energy = change in gravitational potential energy

b) Change in kinetic energy = (1/2) m*Vf² - (1/2) m*Vo²

since Vo = 0, change in kinetic energy = (1/2) m*Vf²

c) Change in gravitational potential energy = m*g*h

∴ (1/2) m*Vf² = m*g*h

m in both sides can be cancelled = > (1/2Vf² = gh = > Vf² = 2gh, which is the same equation used in kinematics.