Mapd An old Biblical story tells of David, a small warrior engaged in man-to- ma
ID: 1795200 • Letter: M
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 = 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 simplicityExplanation / Answer
The rock is released in the second quadrant. The rock must rise because Goliath was quite a bit taller than David. But you are told that you are to ignore gravity and the effect it will have on the rock's trajectory. Good thing because the rock will be affected by gravity, and that makes the problem considerably more difficult.
Too bad this problem has givens in the imperial system. It would be slightly easier to work with in metric.
The circular force has a formula of mv^2/r. If you draw a diagram of this problem, you will see that the rock is released in the second quadrant. The rock is balanced by an upward force of mg*sin(theta) where theta = 4.83 degrees.
so mg*sin(theta) = m v^2/r
r = 5.27 feet/2 = 2.635 feet
g = 32 feet /sec^2
the m's cancel out.
You are solving for v
32 * sin(4.83) = v^2 / 2.635
32 * sin(4.83) * 2.635 = v^2
7.1 feet^2 / sec^2 = v^2
v_vertical = 2.66 feet /sec
This is actually the vertical component of the speed.
The horizontal is v * cos(4.83) which I will leave you to calculate.
Hint
===
If the vertical component of V is 2.66, how do you find the straight line velocity. Use sin(4.83) to do this
2.66 = V * Sin(theta)
This is the velocity that the rock struck Goliath. The horizontal velocity is interesting but not necessary and it is much larger than 2.66.