physics
posted by daniel on .
Two identical cannons fire cannonballs horizontally with the same initial velocity. One cannon is located on a platform partway up a tower, and the other is on top, four times higher than the first cannon. How much farther from the tower does the cannonball from the higher cannon land than the cannonball from the lower cannon?

they both go at the same horizontal speed forever and ever (until they hit)
Therefore we only have to solve a dropping problem
h and 4 h and we want the times in the air
h = (1/2) g t^2
4 h = (1/2) g T^2
t^2 = 2 h/g
T^2 = 8 h/g
T^2/t^2 = 4
so
T/t = 2
so the high one is in the air twice as long
so
It goes twice as far.