A column of air weighs ~1kg/cm^2 (handy!), and the example has a 15km span of "Dense Rock" which I've seen mean "Dense Rock Equivalent" in the Volcanic Explosivity Index, where it has a density of 2,500 kg/m^3. Assuming that, a column of the asteroid is
The kinetic energy per column of the impactor is 1/2mv^2, or 0.5 * 3750 * 80000m/s^2, or
1875 * 6.4e9m^2/s^2
= 1.2e13 Joules
Which is about 20 gallons of gasoline equivalent. As you say, that's absorbed in ~1s (space is 100km up, so 80km/s is just about right). If so that warms up and starts melting the surface of the asteroid, but not much more I guess.
Summary: my initial math checks out for the total KE of the asteroid, and then we used that to look at the surface heating by the compressed atmosphere and then the Fourier heat analysis of conduction into the asteroid surface
Answer: Tho the atmosphere would be heated to 100k degrees and that's 1000x more than needed for vaporization of e.g. granite, the duration of ~1s means that only a few millimeters of surface would be vaporized by the time of impact.
does it give the same answer repeatedly? every time i've tried to solve problems like that with chatgpt i've been given beautifully worded garbage that doesn't commpute by hand, and won't be repeated if I retry the prompt.
A column of air weighs ~1kg/cm^2 (handy!), and the example has a 15km span of "Dense Rock" which I've seen mean "Dense Rock Equivalent" in the Volcanic Explosivity Index, where it has a density of 2,500 kg/m^3. Assuming that, a column of the asteroid is
2500kg/cm^2/(100cm/m * 100cm/m) = .25kg/m * 15km = 3,750kg
The kinetic energy per column of the impactor is 1/2mv^2, or 0.5 * 3750 * 80000m/s^2, or
1875 * 6.4e9m^2/s^2 = 1.2e13 Joules
Which is about 20 gallons of gasoline equivalent. As you say, that's absorbed in ~1s (space is 100km up, so 80km/s is just about right). If so that warms up and starts melting the surface of the asteroid, but not much more I guess.