Question

A 150-g baseball is dropped from a tree 13.0 mabove the ground.

A) With what speed would it hit the ground if air resistance could be ignored?

B) If it actually hits the ground with a speed of 9.00 m/s , what is the magnitude of the average force of air resistance exerted on it?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Part A

Air resistance is ignored.

Mass of the baseball = m = 150 g = 0.15 kg

Height from which the baseball is dropped = H = 13 m

Speed of the ball when it hits the ground = V₁

By conservation of energy the initial potential energy of the ball is converted into it's kinetic energy as it falls down.

mgH = mV₁²/2

gH = V₁²/2

(9.81)(13) = V₁²/2

V₁ = 15.97 m/s

Part B

Air resistance is considered.

Mass of the baseball = m = 150 g = 0.15 kg

Height from which the baseball is dropped = H = 13 m

Speed of the ball when it hits the ground = V₂ = 9 m/s

Average force of air resistance on the ball = F

By conservation of energy the initial potential energy of the ball is equal to the kinetic of the ball at the ground plus the work done against air resistance.

mgH = mV₂²/2 + FH

(0.15)(9.81)(13) = (0.15)(9)²/2 + F(13)

F = 1 N

A) Speed at which the baseball will hit the ground if air resistance is ignored = 15.97 m/s

B) Magnitude of average force of air resistance on the baseball if it hits the ground at 9 m/s = 1 N