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, thereby allowing the projectile to fly in a straight line at high speed. Historically, warriors and hunters typically used a vertical circle, but the circle used here is horizontal for simplicity. In this problem, assume that the sling, when unfolded, was roughly R=5.18 ft in total length and that the rock weighed a half a pound. If David whirled the sling such that the sling was at an angle θ=5.03∘ below the horizontal, with what speed v did the rock strike Goliath? Assume there is no air friction and that the drop in height due to gravity is minimal.
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, thereby allowing the projectile to fly in a straight line at high speed. Historically, warriors and hunters typically used a vertical circle, but the circle used here is horizontal for simplicity.
In this problem, assume that the sling, when unfolded, was roughly R=5.18 ft in total length and that the rock weighed a half a pound.
If David whirled the sling such that the sling was at an angle θ=5.03∘ below the horizontal, with what speed v did the rock strike Goliath? Assume there is no air friction and that the drop in height due to gravity is minimal.
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