An asteroid with mass 250 kg is travelling directly toward the earth. When it is

Question

An asteroid with mass 250 kg is travelling directly toward the earth. When it is 25,000 km from the surface of the earth, it has a speed of 10 km/s. What is its speed when it hits the surface of the earth?

(The mass and radius of the earth are ME = 5.98 × 1024 kg and RE = 6,380 km respectively, and Newton's gravitational constant is G = 6.67300 × 10-11 m3 kg-1 s-2. You should ignore any effects due to air resistance and the rotation of the Earth)

(a)   6 km/s
(b)   11 km/s
(c)   14 km/s
(d)   21 km/s
(e)   25 km/s

Explanation / Answer

here,

mass of asteroid , ma = 250 kg

initial speed , u = 10 km/s

Potentila energy = - G * m * M/distance from centre

using conservtaion of energy

initial PE + initial KE = fianal KE + final PE

0.5 * m * u^2 - G * m * M / ( re + d) = 0.5 * m * v^2 - G * m *M /( re)

0.5 * 10000^2 - 6.673 * 10^-11 * 5.98* 10^24 / ( 6380000 + 25000000) = 0.5 * v^2 - 6.673 * 10^-11 * 5.98* 10^24 / ( 6380000 )

v = 14130.1 m/s

v = 14 km/s

the speed of the asternoid at the surface of earth is (c) 14 km/s

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