David uses a sling to increase the speed of a projectile (in this case a rock),

Question

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 5.63 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 ? = 5.13o 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.) Also, suppose David had missed. How far would the rock travel before striking the ground if David released it from a height of 4.95 ft?

Explanation / Answer

a)

here r = 5.45cos3.93 = 5.437 ft

g = 32.2 ft/s^2

Tsin3.93 = mg----- ------1

Tcos3.93 = mv^2/r -----2

dividing 1 by 2 we get

tan 3.93 = gr/v^2

v = sqrt (gr/tan3.93) = 50.48 ft/s

b)

in y direction

u =0

s = 4.95 ft

S = 1/2gT^2

t = 0.55 sec

in x direction

s = ut = 27.76 ft

therefore distance travelled = 27.76 ft

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