Suppose a fixed cannon is to fire a projectile at an enemy tank, which is moving toward the cannon at a speed of 15 mph. If the cannon is to fire at the moment the tank is 3 miles from the cannon and the muzzle speed of the cannon is 1100 mph, what is the correct equation to determine the firing angle if acceleration is 79000 m /h^2?

Question

Answer: (10.2cos(theta) + 0.139) sin(theta) = 1

I just need help coming up with that answer

Answer 1

You can get your acceleration equation a=<0, -79000> and get your position equation by integrating and using your initial values so you'll get

s(t) = <1100cos(theta)*t, -39500*t^2 + 1100sin(theta)*t>

then set your y component equal to zero to find how long it will take the ball to hit the "ground"(which will be the tank).

Once you have the "t" with respect to theta, you say the tank moves towards you at 15mph and is initially 3 miles away.

so.. its x-position at time "t" will be 3-15*t(where t is the time you found earlier)

You then set that x-position of the tank to the x-position of the cannonball and figure out what theta is needed.

It will most likely give you an equation that looks different than that equation but doing some simple algebra will give you that.