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Skate
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Homework Statement
A person sits on a skateboard and wants to propel themselves. The persons mass is 150 lbm whihile the skateboard mass can be ignored. The person has a bucket with 1 kg rocks totaling 10 kg. The rocks are ejected at a rate of 1 kg/s and a velocity of 108 mph with respect to the skateboarder. The rocks leave the hand at an angle of 15 degrees above the horizontal plane. Assume drag and friction are negligible.
a) Calculate the final velocity of the skateboard
b) From the skateboards perspective, each rock has the same relative velocity as it is thrown. However, since the skateboard is speeding up, it appears to an inertial observer that the velocity of each rock diminishes. Consequently, the kinetic energy of each rock decreases. However, the skateboard gains a constant amount of kinetic energy as each rock is thrown. Explain this paradox and use equations as necessary.
Homework Equations
Conservation of linear momentum
m1v1i + m2v2i = m1v1f + m2v2f
The Attempt at a Solution
Object 1 applies to the person and the skateboard. Object 2 applies to the rocks. m1=68.04 kg (150 lbm), m2=10 kg. I understand that v1i=0 and v2i=108 mph, but I don't understand how to interpret the final speed of the rocks (v2f) in order to find the final speed of the skateboard (v1f) and I also don't know how the 15 degree angle comes into the mix. Any help or advice is greatly appreciated!