Question

# The comet that killed the dinosaurs had an estimated mass of 3.0x1017 kg and was traveling...

The comet that killed the dinosaurs had an estimated mass of 3.0x1017 kg and was traveling at 19 km/s when it hit Earth's surface. Assuming the comet was heading directly towards the earth, estimate its speed (km/s) when it entered Earth's effective gravitational field (a distance of (5.0x108 m away from its center). The radius of the Earth is 6,371 km, and its mass is 5.972x1024 kg.

given
M = 5.972*10^24 kg

R = 6.37*10^6 m

mass of comet, m = 3.0*10^17 kg

vf = 19 km/s = 19000 km/s
vi = ? (at r = 5*10^8 m)

Apply conservation of mechanical energy

PEf + KEf = PEi + KEi

-G*M*m/R + (1/2)*m*vf^2 = -G*M*m/r + (1/2)*m*vi^2

-G*M/R + (1/2)*vf^2 = -G*M/r + (1/2)*vi^2

(1/2)*vi^2 = G*M*(1/r - 1/R) + (1/2)*vf^2

vi^2 = 2*G*M*(1/r - 1/R) + vf^2

= 2*6.67*10^-11*5.972*10^24*(1/(5*10^8) - 1/(6.371*10^6) ) + 19000^2

= 237547842

vi = sqrt(237547842)

= 15412 m/s

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