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Serga [27]
3 years ago
5

A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The asteroid has an estimated mass,

based on its size, of 5×109kg. It is approaching the Earth on a head-on course with a velocity of 660 m/s relative to the Earth and is now 4.0×106 km away. With what speed will it hit the Earth's surface, neglecting friction with the atmosphere?
Physics
1 answer:
Citrus2011 [14]3 years ago
5 0

Answer:

v = 7934.2 m/s

Explanation:

Here the total energy of the Asteroid and the Earth system will remains conserved

So we will have

-\frac{GMm}{r} + \frac{1}{2}mv_0^2 = -\frac{GMm}{R} + \frac{1}{2}mv^2

now we know that

v_0 = 660 m/s

M = 5.98 \times 10^{24} kg

m = 5 \times 10^9 kg

r = 4 \times 10^9 m

R = 6.37 \times 10^6 m

now from above formula

GMm(\frac{1}{R} - \frac{1}{r}) + \frac{1}{2}mv_0^2 = \frac{1}{2}mv^2

now we have

2GM(\frac{1}{R} - \frac{1}{r}) + v_0^2 = v^2

now plug in all data

2(6.67 \times 10^{-11})(5.98 \times 10^{24})(\frac{1}{6.37 \times 10^6} - \frac{1}{4 \times 10^9}) + (660)^2 = v^2

v = 7934.2 m/s

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