An old Biblical story tells of David, a small warrior engaged in man-to-man comb
ID: 2139801 • Letter: A
Question
An old Biblical story tells of David, a small warrior engaged in man-to-man combat with Goliath, a much larger adversary. In the story, David uses a sling to increase the speed of a projectile (in this case a rock), striking Goliath in the forehead and killing him. The type of sling often used in such combat consists of a long strip of cloth with a pouch halfway down its length. The rock is positioned in the pouch, with the warrior holding both ends of the sling. By whirling the sling in a horizontal* circle, a warrior can release one end of the sling, therefore allowing the projectile to fly in a straight line at high speed. In this problem, we will assume that the sling, when unfolded, was roughly 5.93 feet in total length. We will also assume the rock weighed a half a pound. If David whirled the sling to the point where the sling subtended an angle of ? = 4.93o with the horizontal, with what speed did the rock strike Goliath? (Assume no air friction and that the drop in height due to gravity is minimal.)
Part 2
Suppose David had missed. How far would the rock travel before striking the ground if David released it from a height of 4.35 ft? (Assume no air friction.)
please show steps.
Explanation / Answer
u = 0 , g = 9.8 m/s2
h = 4.35 ft = 4.35 x 0.3048 m = 1.32588 m
v^2 - u^2 = 2gh
v^2 = u^2 + 2gh
v = sqrt (u^2 + 2gh)
v = sqrt (2 * 9.8 * 1.32588)
= 5.09