Sledding

As I was driving back to Colgate yesterday night, I noticed a man and his child sledding down the slope in front of the admissions building. I decided to calculate their final velocities when they reached the bottom of the slope. I assumed that the mass of the man is 70kg, the mass of the child is 28kg, mass of the sled is 2kg, and the angle ϴ is 20˚. µ_k of a plastic sled on snow is 0.3.

To find the final velocity of the man:

ΔKE = - ΔPE + W_NC

½ mv_f² = mgh_i + F_fr d cosϴ

½ (72kg) v_f² = (72kg)(9.8m/s²)(4m) + µF_N dcosϴ

½ (72kg) v_f² = (72kg)(9.8m/s²)(4m) + µ(mg cos 20) dcosϴ

½ (72kg) v_f² = (72kg)(9.8m/s²)(4m) + 0.3(72kg*9.8m/s² * cos 20) (5m) cos180

v_f = 7.13 m/s

To find the final velocity of the child:

ΔKE = - ΔPE + W_NC

½ mv_f² = mgh_i + F_fr d cosϴ

½ (30kg) v_f² = (30kg)(9.8m/s²)(4m) + µF_N dcosϴ

½ (30kg) v_f² = (30kg)(9.8m/s²)(4m) + µ(mg cos 20) dcosϴ

½ (30kg) v_f² = (30kg)(9.8m/s²)(4m) + 0.3(30kg*9.8m/s² * cos 20) (5m) cos180

v_f = 7.13 m/s

Thus, both the final velocities of the man and the child are the same.