Was My Approach to Solving the Physics Problem Correct?

[agent_509]

Homework Statement

You are in charge of a cannon that exerts a
force 19000 N on a cannon ball while the ball
is in the barrel of the cannon. The length of
the cannon barrel is 1.92 m and the cannon is
aimed at a 37° angle from the ground.

The acceleration of gravity is 9.8 m/s^2.

If you want the ball to leave the cannon
with speed v0 = 79.3 m/s, what mass cannon
ball must you use?

Homework Equations

W=∫_C F•dx

The Attempt at a Solution

I already have done the problem, the answer is 11.56kg. My question is if the way I solved this problem was ok. i got several points docked for the way I answered it.

I wanted to make sure I understood the concept well enough to apply it to more complex problems, such as ones where the path taken by an object was not a straight line and the force varied with position, so I made the path taken into a vector valued function r(t) where 0≤t≤1 (t is arbitrary since I'm calculating work right?) and then combined the force of gravity with the force exerted by the cannon into a force field existing along the path taken by the cannonball. I calculated dr from the vector-valued function, and solved the line integral. Of course the whole thing only turned out to be the force dotted into the path taken by the cannonball anyways, but I was just trying to make sure I understood the concept.

So my question is this: is there something wrong with the way I solved the problem?

Edit: I meant "work problem" not word problem, my apologies.

 

[Spinnor]

You got the right answer, that is good. Sounds like you made the problem more complicated then it needed to be. Time is money, keep it simple.

 

[agent_509]

I'm aware of that. Like I said I just wanted to make sure I understood how I could solve more complicated versions of the problem. thanks.