An old Biblical story tells of David, a small warrior engaged in man-to-man comb
ID: 1276578 • 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 5.51 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 = 4.43o 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 4.85 ft? (Assume no air friction.)
Explanation / Answer
Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.
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.)
answer
T=tension in sling
X balance
Tcos4.93 = mv^2/(5.93*0.3048*cos4.93/2)....(1)
Y balance
Tsin4.93 = mg....(2)
(1)/(2) gives
cot 4.93 * cos 4.93 * 2.965*0.3048*9.8 = v^2
v=10.114 m/s = 33.18 ft/s
time of flight =v2h/g =0.52 s
distance traveld = 10.114*0.52=5.23m=17.25ft