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 32.1 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 565 N.
(a) What direction should you throw your boot so that you will most quickly reach the shore?


away from the closest shore
straight up in the air
at your friend standing on the closest shore
perpendicular to the closest shore
.

(b) If you throw your 1.13-kg boot with an average force of 430 N, and the throw takes 0.630 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.)
N

(c) How long does it take you to reach shore, including the short time in which you were throwing the boot?
s

Explanation / Answer

Hi,
(a) You should throw your boot in the direction away from the closest shore so that the reaction force is towards the closest shore. (b) The magnitude of the average force you exert on the boot equals the magnitude of the average force the boot exerts on you: Hence Fav on you = 430N (c) The time required for you to reach the shore is the sum of your travel time while accelerating and your travel time while coasting: => t = 0.63 + t'.       acceleration during the time of average force in interaction with shoe is given by          a = Fnet / m = Fav / w/g = Fav * g / w = 430 * 9.8 / 565 = 7.458 m/s^2        We know s = ut + (1/2)at^2. Hence the distance travelled in this short time is given by s = 0 + (0.5 * 7.458 * 0.63^2) = 1.48 m.        After this interaction of time, the final velocity is given by          v = u + at = 0 + (7.458 * 0.63) = 4.6986 m/s.        From here, it will travel with constant velocity towards the shore and the time taken to reach the shore from this instant is given by t' = (x - s) / v                                                                                 = (32.1 - 1.48)/4.6986                                                                                 = 6.5168sec.       Hence the total time taken = t = 0.63 + 6.5168 = 7.1468sec Hope this helps you. Hope this helps you.

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