- #1
Manthegun
- 3
- 0
Homework Statement
To protect his food from hungry bears, a boy scout rasies 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 (v boy), holding the free end of the rope in his hands.
(a) Show that the speed v of the food pack is given by (x)(x^2 + h^2)^(-1/2)(v boy) where x is the distance he has walked away from the vertical rope
The diagram given is something like this,
|\
| \
| \
| \
| \
|___\ ------------->
* The diagram is not coming out properly, anyhow its a right angled triangle. with the below characteristics.
*h is the constant distance between the tree top and the hand of the boy (the vertical line)
*x is the variable horizontal distance (the horizontal line)
*The point where the diagonal and vertical line meet is like the "pivot". That is where the rope goes one round around a twig.
* ----> is v boy
Homework Equations
The Attempt at a Solution
V = distance displaced / time
Distance displaced = (h^2 + x^2)^(1/2) - h
Assumption ? < The change in diagonal length when the boy moves = distance displaced >
According to Pythagoras theorem the above (h^2 + x^2)^(1/2) is derived. And the change being the ( final diagonal distance - initial diagonal distance (when x=0) ).
So I have come until this point, but I am unable to simplify it further so that its similar to the equation I'm supposed to derive. Can anyone hint to me or guide me along on which part I have made a mistake or what's the possible next step? Thanks
P.s: hope the drawing helps. If any additional information is needed do tell me so that i can take a look and see whether its provided. A BIG THANKS again.