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Problem 35 Hard Difficulty

An asteroid with a diameter of 10 $\mathrm{km}$ and a mass of $2.60 \times 10^{15} \mathrm{kg}$ impacts the earth at a speed of 32.0 $\mathrm{km} / \mathrm{s}$ landing in the Pacific Ocean. If 1.00$\%$ of the asteroid's kinetic energy goes to boiling the ocean water (assume an initial water temperature of $10.0^{\circ} \mathrm{C} ),$ what mass of water will be boiled away by the collision? (For comparison, the mass of water contained in Lake Superior is about $2 \times 10^{15} \mathrm{kg.} )$

Answer

$5.05 \times 10^{15} \mathrm{kg}$

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Physics 101 Mechanics

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Video Transcript

Let's take a look at the question. The question was asking us how much water will be boiled off if the asteroid hit Ana Pacific Ocean. Okay, so while that's for you, Allah can energy over the asteroid which have and we squared. We know the mass of the asteroid is 2.6 times sent about 15 Cuba and the velocities of 32 kilometers per sec. Uh oh. Sorry. Yeah, you owe me two per second. OK, so can I. Am's. You have equal to well half times. 2.6 times to tend to Apollo 15 kilograms. Time. 32 kilometers per second, which is 32 times. Tend to Ah, our three meter per second. Because one killed me is 10 toe. How power of three year. Okay and square. And this would give us one boy 3312 times tend to a power 24 to okay. And was talking about on the 1% of massage. And as you boil your water, so 1% was 0.1 Has the can I the Amazon? We have. He will give us 1.3312 times potential power 22 June. Okay, so now into Vega how mush waterboy off. So the mass water we don't know. Well, we can theory out through a formula which is Q equal to M c doesn t plus and no, the m c don't that he hear is the heater require to raise, uh, to to change the temperature. Ok, And the m one here I'm outta here is just, uh they didn't he times the mass? Okay, Because you're too boy the water. Remember, the initial temperature was 10 degrees Celsius, so you have to boil the water. The water must reach 100 degrees Celsius because that's the boy with points. So later here being wolf as a part of the transformation from the liquid to heat until to the Tokyo gas. Because when you boil the water, water will turn into a gas like water vapour. No. So, okay, this work, how are conclusion here? So we get and we just simply equals a Q over. See Donna T plus l So cue or you know which is 1.3312 tests 10 to the power between two ju. Okay, See? So the service iffy water is 41 90 ju perfect. Your grand times. The degree Celsius. Okay, Anton, start changing temperature. So it seems, is far 10 degrees houses to 100 degrees Celsius. So just 90 degree cells. That's the change in temperature and positive. Later heats water to boil. And that that's 2256 times. Tend to about three at you. Her killer Where? Okay, after all these calculations, you give us a mass is equal to by point 06 ties. 10 to the power off. 15 kilograms. So this is how much water we boiled off. If the story he on a Pacific Ocean. Okay, thank you.

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