Solve Momentum Problem for Dan on Skateboard

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The discussion focuses on solving a momentum problem involving Dan on a skateboard, utilizing the equation for final velocity after a collision. The equation presented is ||\vec{v}_{f}||=\frac{1}{m_{1}+m_{2}}\sqrt{(m_{1}v_{1}-m_{2}v_{2}\cos(30))^{2}+m_{2}^{2}v_{2}^{2}\sin^{2}(30)}. Given Dan's mass of 40.0 kg and the skateboard's mass of 5.00 kg, the problem requires calculating Dan's velocity as he jumps backward off the skateboard, which is moving at 3.00 m/s and kicks forward at 8.00 m/s. Understanding the conservation of momentum is crucial for solving this problem.

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techtrailer89
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This is an equation I found in the achieve can anyone explain what this means
||\vec{v}_{f}||=\frac{1}{m_{1}+m_{2}}\sqrt{(m_{1}v_{1}-m_{2}v_{2}\cos(30))^{2}+m_{2}^{2}v_{2}^{2}\sin^{2}(30)}
here is the problem Dan is gliding on his skateboard at 3.00 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.00 m/s (as measured by an observer on the ground). Dan's mass is 40.0 kg and the skateboard's mass is 5.00 kg. How fast is Dan going as his feet hit the ground?
I am just not sure which equation to use.
 
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