Calculating Cannon Ball Barrel Length: Impulse and Velocity

AI Thread Summary
The discussion revolves around calculating the barrel length of a cannon for a human cannonball based on impulse and velocity. The impulse is given as 2.5 x 10^3 N·s, and the mass of the cannonball is 65 kg. The user attempted to find the acceleration using the formula J=ma(delta t) and calculated a distance of 3.85 m, but found this answer to be incorrect. Clarification is sought on how to derive the time of 0.2 seconds, which is essential for solving part b of the question. The conversation emphasizes the need to correctly apply the equations of motion to determine the barrel length.
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Homework Statement



The impulse on a human cannon ball is 2.5  103 N·s. The cannon
ball has a mass of 65 kg.

Homework Equations



How long is the barrel of the cannon if the cannon ball leaves the
cannon at 120 km/h?

The Attempt at a Solution



I used the formula J=ma(delta t)
(2.5x 10^3)=(65)(a)(0.2)

to find the acceleration. Then, I used the formula d=v1(t)+(1/2)(a)(t^2) to find the distance, and I got 3.85 m, but the answer at the back is wrong.

Can anybody help me?
 
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How did you get the time of 0.2 seconds ?
 
That's given in part a of the question, which I already got. Here's the entire question:

The impulse on a human cannon ball is 2.5  103 N·s. The cannon
ball has a mass of 65 kg.
a) What force does the cannon exert on the human cannon ball if
it takes 0.2 s for the human cannon ball to leave the cannon?
b) How long is the barrel of the cannon if the cannon ball leaves the
cannon at 120 km/h?
 
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