Variable acceleration

[esmmajor]

1. Problem Statement:
A fixed cannon is to fire a projectile at a tank moving toward the cannon at 40 mph. If the cannon is to fire at the moment the tank is 8 miles from the cannon, and the muzzle speed of the projectile is 1000 mph what is the correct equation to determine the firing angle?


2. Homework Equations :
Acceleration of gravity: 79000 m/h^2


3. Solution Attempt:

Initial conditions:
r=<8-40t,0>
v=<1000*cos(theta), 1000*sin(theta)>

started with:
acceleration_projectile=<0,-g>
<0,-79000.
velocity (took integral and used initial conditions to come up with constants)
v=<1000*cos(theta), -79000t+1000*sin(theta)>

position:
r=<1000*cos(theta)*t+t-40t, -79000t^2/2+1000*sin(theta)t>

**The answer I'm supposed to get is (3.16*cos(theta)+0.127)*sin(theta)=1

Any help would be greatly appreciated.

 

[millitiz]

Hi, esmmajor.
Well, you are right for every step. Except that, at some point, you want to eliminate t.
My personal suggestion would be:
in x direction, how would you relate the velocity of the particle to the time and distance?
and in y direction, how are you going to relate the initial velocity to the acceleration and time?
And finally, are these two time t, equal?
Have an idea of how to eliminate the t?