Question

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.

Answer 1

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

= 15.4 km/s <<<<<<<-------------------Answer