3). You are sitting in a sled at rest on a pond covered with nice, thick, fricti

Question

3). You are sitting in a sled at rest on a pond covered with nice, thick, frictionless ice. Your own mass is 92 kg and the mass of the sled when empty is 15 kg.

a) From shore, someone throws a baseball of mass 0.12 kg to you, and you catch it; the horizontal component of the ball's velocity is 39.7 m/s. What wil be the sled's and your speed with respect to the surface of the pond after you catch the ball? Note: Your answer should be in centimeters per second.

b). Different situation: suppose you are in the sled and it's alreadt moving to the west, at a speed of 3.3 cm/s. From the southern shore, your friend again throws a baseball of a mass of 0.12 kg, which you catch as it's traveling northward with a horizontal velocity component of 39.7 m/s. In this case, what will be the sled's and your speed after catching the ball?

c). Once again, suppose you start at rest on the sled out on the pond. Suddenly, you jump off of the sled, after which the empty sled is traveling at a speed of 1.2 m/s. What will be your speed on ice after jumping off ( Note: this will be the same as the horizontal component of your velocity just as you jump)

d). That empty sled is still moving at 1.2 m/s. A parachutist of a mass of 77 kg suddenly drifts straight vertically down from a helicopter landing on the sled. What will be the sled's speed in the parachutist after he lands?

Explanation / Answer

a) mass of the system before catching the ball = 92+15=107kg

mass after catching =0.12+107=107.12kg

momentum before catching=0.12*39.7=4.764 kgm/s

momentum after catching=107.12v

by conservation of momentum

107.12v=4.764

v=0.044m/s=4.4cm/s

b)here momentum of before catching =107*3.3/100 - 4.764=-1.233kgm/s

momentum after catching = 107.12v

107.12v=1.233

v=0.115m/s=11.5cm/s

c) momentum before jumping=0

momentum after jumping = 92v+15*1.2

by conservation of momentum

92v+15*1.2=0 or v=0.196m/s

d)

by coservation of momentum

15*1.2= (15+77)v

v=0.196m/s

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