A highly motivated Einesteinium DeGroot swings on a vine to rescue a hot babe fr

Question

A highly motivated Einesteinium DeGroot swings on a vine to rescue a hot babe from an unspeakable death, scooping her into his arm at the bottom of his swing and taking her up to safety on a ledge. DeGroot, being a college professor with some knowledge of physicis, calculated wheter the maneuver was possible before he attempted it---a calculation you should try using the following information. DeGroot's mass including his hockey stick (snake protection) was 70. kg, the hot babe's mass was 48.0 kg, and the ledge from which he starts is 8.00 m above the low point of the swing. (a) what is DeGroot's velocity just before he scoops up the hot babe, assuming he starts from the rest? (b) what is their velocity just after scopping her up? (c) How much kinetic enery is lost in their colllision? (d) What is the highest ledge they can swing up?

Explanation / Answer

a) conservation of energy

1/2 mv^2 = m g h

v = sqrt(2 g h) = sqrt(2*9.81*8)=12.53 m/s

b) conservation of momentum

70*12.53 = (70+48)*v

v= 70*12.53/(70+48)=7.43 m/s

c) loss = Kei -Kef = 0.5*70*12.53^2 - 0.5*118*7.43^2=2238 J

d) Ei = Ef

1/2 mv^2 = m g h

h = v^2/(2 g ) = 7.43^2/(2*9.81)=2.81 m

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