An old Biblical story tells of David, a small warrior engaged in man-to-man comb
ID: 2289147 • 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 5.24 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 ? = 4.53o 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.)
2-Suppose David had missed. How far would the rock travel before striking the ground if David released it from a height of 4.25 ft? (Assume no air friction.)
Explanation / Answer
T=tension in sling
X balance
Tcos4.25 = mv^2/(5.24*0.3048*cos4.25/2)....(1)
Y balance
Tsin4.25 = mg....(2)
(1)/(2) gives
cot 4.25 * cos 4.25 * 2.62*0.3048*9.8 = v^2
v=10.248 m/s = 33.622 ft/s
time of flight =v2h/g =1.12 s
distance traveld = 10.248 * 1.12= 11.477m = 37.65 ft
I answerd both in ft and m.
hope this helps.
cheers!