(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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 whats 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.

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# Homework Help: Kinematics problem

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