An adventurous camper (77 kg) finds him/her self stranded in the middle of a fro

Question

An adventurous camper (77 kg) finds him/her self stranded in the middle of a frozen lake (diameter = 1.5 km) with only a bag of rocks (total mass 12.0 kg). The ice is so slippery, that they move about the lake's surface without friction (don't ask me how they got there in the first place). Remembering what they learned in a physics lab, they devise a way to get themselves to the edge of the lake by throwing the bag of rocks in the opposite direction of the shore with a velocity of 6.0 m/s. If they throw the rocks all at once, how long does it take for them to slide to shore?

Explanation / Answer

To find out the velocity of the camper, apply conservation of momentum -

m1*v1 = m2*v2

=> 12*6 = 77*v2

=> v2 = (12*6)/77 = 0.935 m/s.

This is the velocity of the camper.

Since the camper is at thecenter of the lake, so time taken by him to reach at the shore -

t = (d/2) / v2 = (1500/2) / 0.935 = 750/0.935 = 802.1 s

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