Conservation of momentum on bike

AI Thread Summary
To solve the problem of conservation of momentum, the initial momentum of the system (Tony, bike, and pack) must equal the final momentum after the pack is thrown. The correct approach involves calculating the velocities relative to the system's center of mass. The initial momentum is calculated as the combined mass of Tony and the bike moving at 1 m/s, while the pack's speed must be adjusted to account for its relative speed of 5 m/s. The mistake in the initial attempt was likely in the application of the momentum equation or in not properly accounting for the relative speed of the pack. Understanding the relative motion is crucial for solving this type of problem.
Momentum09
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Homework Statement



Tony (45kg) coasts on his bike (5kg) at a constant speed of 1 m/s, carrying a 5kg pack. Tony throws his pack forward, in the direction of his motion, at 5 m/s relative to the speed of bike just before the throw. What is the bike speed immediately after the throw?

Homework Equations



mv1 + mv1 = mv2 + mv2


The Attempt at a Solution



I combined Tony and the bike's mass together, 50kg. I then did
(50)(1) + (5)(1) = (50)(v) + (5)(5) and solved for v. However that wasn't correct. Can somebody please tell me what I did wrong?

Thank you so much!
 
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Please read the following carefully.

Momentum09 said:
at 5 m/s relative to the speed of bike

Relativity is your friend. :wink:
 
thanks so much! :)
 

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