Did I do this question correctly?

[andgabbana]

I just want to make sure I know I'm on the right track...

A human cannonball with a mass of 70kg experiences an impulse of 4.0x10^3 N*s for 0.35s

a) Calculate the force acting on the human 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.)a) J = F (delta t)
4.0x10^3 = F (0.35)
F = 11428.57

b) J = delta P = 4.0x10^3
delta P = mv(f) - mv(i)
4.0x10^3 = 70 * V(f)
V(f) = 57m/s

E(k) = 0.5[mV(f)] - 0 ----- because it was at rest
=0.5(70 x 57)
=1995

F d = E(k)
11428.57 x d = 1995
d = 5.72m

therefore it was 5.7m long?

 

[ImAnEngineer]

I just want to make sure I know I'm on the right track...

A human cannonball with a mass of 70kg experiences an impulse of 4.0x10^3 N*s for 0.35s

a) Calculate the force acting on the human 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.)a) J = F (delta t)
4.0x10^3 = F (0.35)
F = 11428.57

b) J = delta P = 4.0x10^3
delta P = mv(f) - mv(i)
4.0x10^3 = 70 * V(f)
V(f) = 57m/s

E(k) = 0.5[mV(f)] - 0 ----- because it was at rest
=0.5(70 x 57)
=1995

F d = E(k)
11428.57 x d = 1995
d = 5.72m

therefore it was 5.7m long?

E_k_i_n=\frac{1}{2}mv^2. You forgot to square!

Other than that you are certainly on the right track. What you are doing is right in principle.

By the way, there is an alternative shorter answer to the problem. You know that there was a constant force acting on the mass, and you know the final velocity, so you can calculate the average velocity. You also know \Delta t so you can calculate \Delta x.