How Do You Calculate the Original Velocity of a Cannonball in a Collision?

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To calculate the original velocity of the cannonball, the conservation of momentum principle is applied, where the momentum before the collision equals the momentum after. The equation used is m1v1 + m2v2 = (m1 + m2)v', where v' is the final velocity of both objects moving together. In this case, the cannonball's mass is 30 kg, the block's mass is 150 kg, and they move together at 4 m/s after the collision. The correct calculation shows that the original velocity of the cannonball is 24 m/s, confirming that adding the final velocity to the calculated value is not the correct approach. Thus, the original velocity of the cannonball is determined to be 24 m/s.
sweedeljoseph

Homework Statement


A 30 kg cannonball strikes a 150 kg stationary wooden block and embeds itself in the block. The block and cannonball move together at 4 m/s. What was the original velocity of the cannonball?

Homework Equations


m1v1=m2v2

The Attempt at a Solution


using the equation i gave i got:

30v=150(4)
v=20

the answer my teacher my teacher gave me was 24 m/s. and i was thinking if you add the '4 m/s' to the velocity i just found it would be '24 m/s'. but i don't know if that was right. i was thinking it might be right because they both moved together after the ball hit the wood for 4 m/s. so is that right? or am i supposed to do something else?

thank you!
sweedeljoseph
 
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The mass after the collision would be the masses of both objects added together since they are now considered to be one object moving at the same velocity.

m1V1 + m2V2 (equals 0) = v'(m1 + m2)

Solve for V1 before
 
so i was right? you add the '4 m/s' to the velocity that i found?
 

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