Posted by MarkB_MI on November 23, 2014 at 05:35:54 from (70.194.12.162):
In Reply to: OT--Physics Question posted by Jiles on November 22, 2014 at 18:41:03:
I realize I made a mistake in my earlier analysis. The projectile fired at 45 degrees won't go as high as the one shot vertical, because its velocity has both horizontal and vertical components. Only half of its kinetic energy is vertical, so it only goes half as high as the one shot vertical. If we approximate the parabolic path of the projectile as a circular arc, the distance traveled by the 45 degree projectile is pi x 1/2 x h, where h is the apogee of the vertical projectile. So the total distance travelled by the 45 degree projectile is about 1.6 times the maximum elevation of the vertical projectile. But the vertical projectile travels twice its maximum elevation so it beats the 45 degree projectile by about 25 percent.
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