In the future, it may become economical to minenear-earth asteroids for their me

Question

In the future, it may become economical to minenear-earth asteroids for their metals, like iron, nickel, titanium,platinum and cobalt (Fig. 3). You are floating near such anasteroid when you notice that your spacesuit thrusters are broken.Fortunately you are carrying a flashlight and pickaxe, each with amass m = 2.00 kg. Your mass is M = 80.0 kg. If you exert a force onthem by throwing them toward the asteroid, they will exert an equaland opposite force on you, pushing you back toward your spaceshipand safety (Fig. 4). You need to reach escape velocityvesc = 0.250 m/s inorder to break free of the asteroid’s gravity, so it’scritical to gain the highest possible speed. Which of the followingshould you do?

(a) Throw both tools at once.

(b) Throw one tool first, reasoning that thiswill make you lighter overall, so that throwing the second toolshould then have a greater effect.

[HINTS: Apply conservation ofmomentum.

Explanation / Answer

suppose you throw the objects with velocity v.. you are at rest in the beginning. CASE 1: throw both together: 2m*v=M*x ( where x is your velocity ) x=2*2*v/80 =0.05v CASE2: throw one at a time... mv=Mx x=2v/80    =0.025v now again, throw the second object in the same direction: (m+M)x=mv+My (where y is the final velocity) 82*0.025v=-2v+80y 2v=-2v+80y y=0.05v same as case 1... therefore, the result is the same so do either...

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