Question

Mapd 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 fy in a straight line at high speed In this problem, we will assume that the sling, when unfolded, was roughly 5.27 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 θ = 4.83° 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.) Number mph A typical break shot in pool (the opening shot) is about 20 mph with a ball that is about half the weight of the rock in the story. Considering this, what impact do you think a half-pound rock traveling at the above calculated speed would have on someone if struck in the forehead? The impact would hurt a little but would likely not cause any injury The impact would likely cause serious injury 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.) Number ft * Warriors and hunters typically use a vertical circle. We have chosen a horizontal circle for simplicity

Answer 1

The centripetal force is balanced by a component of its wieght (mgsin(θ))

mv2/r=mgsin(θ)

r=5.27/2 =2.635 ft

g= 32 ft/s2
solving for v

v= sqrt(rgsin(θ))

v=sqrt(2.635*32*sin(4.83))

v=2.664 ft/s

This is the vertical component of velocity

To find straight line velocity, V

V*sin(θ)=2.664

V=31.639 ft/s

V= 21.565 mph

The impact would likely cause serious injury

horizontal distance,R=u*sqrt(2*h/g)

R=31.639*sqrt(2*4.85/32)

R=17.419 ft