Because of your physics background, you have been hired as a technical advisor f

Question

Because of your physics background, you have been hired as a technical advisor for a new James Bond adventure movie. In the script, Bond and his latest love interest, who is 2/3 his weight (including skis, boots, clothes, and various hidden weapons), are skiing in the Swiss Alps. She skis down a slope while he stays at the top to adjust his boot. When she has skied down a vertical distance of 100 m, she stops to wait for him and is captured by the bad guys. Bond looks up and sees what is happening. He notices that she is standing with her skis pointed downhill while she rests on her poles. To make as little noise as possible, Bond starts from rest and glides down the slope heading right at her. Just before they collide, she sees him coming and lets go of her poles. He grabs her and they both continue downhill together. At the bottom of the hill, another slope goes uphill and they continue to glide up that slope until they reach the top of the hill and are safe. Both Bond and his girl friend are using new, top-secret frictionless stealth skis developed for the British Secret Service. The writers want you to calculate the maximum possible height that the second hill can be relative to the position where the collision took place. What is that height?
m

Explanation / Answer

So first we need to find the velocity of bond when he reaches the girl

PE=KE
mgh=(1/2)mv2

v=(2gh)=(2*9.8*100)

v=44.27 m/s

Now the veloicty when they are togther

mv= (m+2m/3)v1

v1=v(3/5)

v1=26.56 m/s

Now we need to find the energy of this and see what height would give an equal potential

(1/2)mv12=mgh

h=(1/2)v12/g

h=36 m

So the new hill can be 36 m higher than the spot where the girl has stopped (this is 64m below the first hill)

Hope that helps

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