Calculating Velocity after Skateboard Jump - A Physics Problem

AI Thread Summary
Dan jumps backward off his skateboard while gliding at 3.00 m/s, causing the skateboard to move forward at 6.00 m/s. The relevant physics equation involves initial and final velocities, as well as the mass of Dan and the skateboard. An attempt to calculate Dan's final velocity resulted in an incorrect answer of 2.29 m/s, leading to confusion about the correct use of the explosion velocity (vexplosion). The correct final velocity for Dan, as he lands, is 2.63 m/s, indicating a misunderstanding in applying the equation. Clarification on the proper method to calculate the final velocity is needed for accurate problem-solving.
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Homework Statement


Dan is gliding on his skateboard at 3.00m/s . He suddenly jumps backward off the skateboard, kicking the skateboard forward at 6.00m/s (as measured by an observer on the ground). Dan's mass is 40.0kg and the skateboard's mass is 5.00kg . How fast is Dan going as his feet hit the ground?

Homework Equations


vf-vi=vexplosion*ln(mf/mi)

The Attempt at a Solution


vi=3 m/s
mi=45 kg
mf of dan=40 kg
I used 6 m/s as vex
when I plugged the above in the equation to find vf I got 2.29 which was marked wrong. Is it wrong to use 6m/s for Vex?
 
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The correct answer is 2.63 m/s, but I'm still confused on the process to get the answer
 

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