On February 15, 2013, asteroid 367943 Duende made a close flyby past the Earth,

Question

On February 15, 2013, asteroid 367943 Duende made a close flyby past the Earth, coming within 27,700 km of the surface (twice the earth's diameter). The asteroid is about 45 meters in diameter.

Let us consider what would have happened if the asteroid had hit the Earth.  You may assume that the asteroid’s mass is 130 million kg, and its velocity when it was very far from the Earth was 6.1 km/s.

a) Calculate the kinetic energy of the asteroid, if it were to strike the Earth’s surface.  (You may ignore the influence of the atmosphere and other solar system objects.)
b) Calculate the final velocity of the asteroid, just before it struck the Earth.
c) If it hit the Earth, all of the asteroid’s kinetic energy would be transformed into an explosion.  For comparison, the “Little Boy” nuclear bomb detonated over Hiroshima released 6.3 x 10^13 joules of energy.  How many Hiroshima nuclear bombs would the impact of 367943 Duende be equivalent to?

Explanation / Answer

a> gravitational force will increase the velocity of the asteroid when it start coming to the earth, this increase in velocity can be find as -

a = F/m

a = GM/x

where M = mass of earth

x = distance b/w two objects

v dv/dx = GM/x2

v dv = GM dx/x2

0.5 v2 = - GM/x

0.5 v2 = GM/27700*1000

M = 6*1024 KG

v = 5375.43 m/sec

net velocity = 6100 + 5375.43

V = 11475.43 m/sec

kinetic energy of the asteroid = 0.5 mV2

K = 8.56*1015 JOULE

sO NUMBER OF EQUIVALENT LITTLE BOY = 135.86

n = 136

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