How Fast Does Howard Fly from the Cannon?

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Howard the Human Projectile is launched from a 300 kg circus cannon during a performance, and the discussion focuses on calculating his initial velocity after being fired. The cannon recoils at a velocity of 2.5 m/s, and momentum conservation principles are applied to determine Howard's speed. The momentum before the launch is zero, as both the cannon and Howard are stationary, meaning their post-launch momenta must also sum to zero. The calculation involves understanding that the momentum of Howard moving forward equals the momentum of the cannon moving backward. The final conclusion points towards the need for precise calculations to find Howard's exit velocity, which is a critical aspect of the discussion.
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The amazing 'Howard the Human Projectile' is fired straight forward from a 300 kg circus cannon during a recent Ringling Bros. Barnum and Baily performance in La Plata. Howard has a mass of 75 kg and the cannon recoils with a velocity of 2.5 m/s, at what initial velocity does Howard leave the cannon?




a. 2.5 m/s

b. 10 m/s

c. 25 m/s

d. 187.5 m/s

I am completely stuck ):
 
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momentum is conserved
the momentum of howard going forward = momentum of cannon going backwards
 
Note that initially, the cannon+Howard have no velocity, and so zero momentum. So the sum of the momenta of the cannon and Howard afterward also has to equal zero, so that you conserve momentum (initial=final). Be sure to keep tabs on your directions (Howard moves opposite the direction of the cannon) because momentum is a vector (but you're dealing with one dimension, which simplifies it a bit).
 
If 300kg object moved backward at the rate of 2.5m/s, then how far did a 75kg object move back?

(2.5/75)*300
 

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