As a prank, your friends have kidnapped you in your sleep, and transported you o

Question

As a prank, your friends have kidnapped you in your sleep, and transported you out onto the ice covering a local pond. When you wake up you are 30.3 m from the nearest shore. The ice is so slippery (i.e. frictionless) that you cannot seem to get yourself moving. You realize that you can use Newton's third law to your advantage, and choose to throw the heaviest thing you have, one boot, in order to get yourself moving. Take your weight to be 605 N. What direction should you throw your boot so that you will most quickly reach the shore? perpendicular to the closest shore away from the closest shore at your friend standing on the closest shore straight up in the air If you throw your 1.31 kg boot with an average force of 410 N, and the throw takes 0.645 s (the time interval over which you apply the force), what is the magnitude of the force that the boot exerts on you? (Assume constant acceleration.) How long does it take you to reach shore, including the short time in which you were throwing the boot?

Explanation / Answer

a)

You need to throw the boot away from the nearest shore so that by momentum conservation, you move closer to the shore

b)

change in momentum of the boot = impulse = force * duration

= 410*0.645

= 264.5 N.s

So, change in momentum of yourself = -264.5

So, the force on you = -264.5/0.645 = -410 N <---- direction is opposite but magnitude is same

c)

change in momentum = 264.5 = m*v

So, v = 264.5/ (605/9.8) <---- mass, m = 605/9.8 kg

So, v = 4.28 m/s <----- speed attained by you

So, time taken to reach the shore = 30.3/4.28 = 7.08 s <------answer

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