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Mr. Rogers' AP Physics C: Projectile motion Problems |
Anti-Balloon Gun Problem
An observation balloon floats over the Enemy lines and the defenders decide to shoot it down. The defending gunners determine the balloon is 3015 m above the ground at a distance of 5000 m. They fire a cannon at an angle of 40° with respect to the horizon with an initial velocity of 760 m/s.
Solution
Place the origin at the bottom of the anti-balloon gun. Define horizontal as the x-dimension with negative to the left and vertical as the y-dimension with negative downward.
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x-dimension
vox = vo cos q = (760 m/s) cos 40° = 585 m/s
x = 1/2axt2 + voxt = 0 + voxt Solving for time gives: t = x / vox = (5000 m) / (585 m/s)
Finish in y-dimension >>> |
y- dimension
voy = vo sin q = (760 m/s) sin 40° = 488 m/s y = 1/2ayt2 + voyt = 1/2 (-9.8 m/s2)(8.55 sec)2 + 488 m/s)(8.55 sec)
While the actual height is 3815 m the cannon shell will destroy the balloon if the fuse is set so that it explodes 3814 m off the ground.
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Typically the gun crew would be able to measure the range and height, but they would have to calculate the angle. Air resistance and wind would complicate the situation.