Artillery Cannon Shoots Down Its Own Shell
An artillery cannon has a muzzle speed (initial shell speed) of 1000 meters per second. It fires its first shell from ground level at an angle of 70 degrees with respect to the horizontal. After reloading, it fires its second shell 30 seconds later at a different angle. The second shell is fired in such a way that it intercepts the first shell in mid air. Determine the angle (in degrees) at which the second shell was fired. The gravitational acceleration is .
The answer is 63.32.
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1 solution
Here's a rough guide toward solving (my solution, at least):
1) Equate the expressions for the x and y coordinates of the first and second shells at the interception time. The interception time is as of yet unknown. The firing angle of the second shell is also unknown.
2) Derive a quadratic expression for the interception time and solve it. Getting to the quadratic expression involves much tedious algebra (at least the way I did it). I ended up squaring the equations and using the property that sin^2 = 1 - cos^2.
3) Knowing the interception time, it is simple to solve for the second firing angle (63.32 degrees).