# Impulse on and the distance traveled by a cannonball

#### benca

Homework Statement
A cannonball with a mass of 70 kg experiences an impulse of 4.0 x 10^3 N*s for 0.35 s

a) calculate the force acting on the cannonball

b) How long was the barrel of the cannon?. Assume the force is applied only for the period of time that the cannonball is in the cannon.
Homework Equations
J = Ft
W= Fd
J = mv' - mv
a)
F = J/t
F = 4000 N*s / 0.35 s
F = 11429 N

b) I was going to equate impulse to the change in momentum and solve for v' (final velocity). Then use v' to solve for ΔEk. set ΔEk = Fd and solve for d. (The question never mentioned an angle of inclination, so I thought it would be ok to use W = Fd)

However when I was isolating v' I realized I wasn't sure what v (initial velocity) was. Is it 0 m/s?

I can solve for Δv using J = ΔP = mΔv (right?) But I'm not sure what I could do with that without knowing either the initial or final velocity. Basically, I'm not sure whether I can use 0 m/s for initial velocity or not.

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#### PeroK

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Homework Statement: A cannonball with a mass of 70 kg experiences an impulse of 4.0 x 10^3 N*s for 0.35 s

a) calculate the force acting on the cannonball

b) How long was the barrel of the cannon?. Assume the force is applied only for the period of time that the cannonball is in the cannon.
Homework Equations: J = Ft
W= Fd
J = mv' - mv

a)
F = J/t
F = 4000 N*s / 0.35 s
F = 11429 N

b) I was going to equate impulse to the change in momentum and solve for v' (final velocity). Then use v' to solve for ΔEk. set ΔEk = Fd and solve for d. (The question never mentioned an angle of inclination, so I thought it would be ok to use W = Fd)

However when I was isolating v' I realized I wasn't sure what v (initial velocity) was. Is it 0 m/s?

I can solve for Δv using J = ΔP = mΔv (right?) But I'm not sure what I could do with that without knowing either the initial or final velocity. Basically, I'm not sure whether I can use 0 m/s for initial velocity or not.
Where are you getting these problems? This is another very poor question. The problem mentions nothing about constant force. Without assuming constant force the problem is not well posed.

Moreover, it's almost certain that the force would be far from constant. The ball would likely accelerate rapidly and reach close to its maximum speed long before it emerges from the barrel. You can look this up online, if you are interested.

Assuming that a cannonball fired by a cannon starts at rest is perhaps a logical and sensible assumption, don't you think? That should be the least of the issues with this problem.

#### benca

It's from an adult high school course I'm taking. There are no formal lectures, just small lessons I need to hand in. I don't know about other adult learning centres but I found out that this one is notorious for it's poor material quality, almost every lesson so far has had either outright mistakes or questions that are poorly phrased. (that's me venting)

anyways, I'll assume it starts at 0 m/s, thanks