To protect his food from hungry bears, a boy scout raises his food pack with a rope that is thrown over a tree limb at height h above his hands. He walks away from the vertical rope with constant velocity vboy, holding the free end of the rope in his hands (Fig. P2.71).
(a) Show that the speed v of the food pack is given by x(x 2 + h)-1/2 vboy where x is the distance he has walked away from the vertical rope.
(b) Show that the acceleration a of the food pack is h2(x 2 + h2)-3/2 v 2 boy .
(c) What values do the acceleration a and velocity v have shortly after he leaves the point under the pack (x = 0)?
(d) What values do the pack’s velocity and acceleration approach as the distance x continues to increase?