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**

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