Question

You are stranded in the middle of a frozen pond, 825 m in diameter which is so slippery that your feet slide freely and don't move you. In desperation you write an S.O.S. on your hat, mass 0.6 kg, and fling it towards the north with a velocity of 13 m/s at 54o with the horizontal. If your mass is 62 kg, how long does it take you to reach the shore? (in hours)

Answer 1

Úse conservation of momentum:
determine the horizontal velocity of the hat.

masshat*velocityhat=massbody*velocitybody

solve for thevelocity of his body. Then, use d=rt to solve for time

Answer 2

horizontal momentum of hat = .6*13 * cos 54 = 4.58 kg m/s North

Your horizontal momentum is the same, but to the South
m V = 62 V = 4.58
V = .0739 m/s
Radius = 412 m
distance = rate * time
412 = .0739 t
t = 5572 seconds
5572 s * 1 hr/3600 s = 1.55 hr.
Hope there is no wind