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larisa86 [58]
3 years ago
15

A small asteroid that has a mass of 100 kg is moving at 200 m/s when it is 1000 km above the Moon. 1) How fast will the meteorit

e be traveling when it impacts the lunar surface if it is heading straight toward the center of the Moon
Physics
1 answer:
Georgia [21]3 years ago
5 0

Answer:

v = 200.005 m / s

Explanation:

For this exercise we can use the concept of energy conservation,

Starting point. When the asteroid at h = 1000 km = 1 10⁶ m

               Em₀ = K + U = ½ m v₀² - G m M / (R + h)

Final point. When the asteroid is on the surface of the moon

              Emf = K + U = ½ m v² - G m M / R

As there is no friction the energy is conserved

             Em₀ = Emf

             ½ m v₀² - G m M / (R + h) = ½ m v² - G m M / R

            ½ m (v₀² –v²) = G m M (-1 / R + 1 / R + h)

            ½ (v₀² - v²) = G M (-h / R (R + h))

            v² = v₀² + 2 G M h / R (R + h))

Let's calculate

           v² = 200² + 2 6.67 10⁻¹¹  7.36 10²² / 1.74 (1.74  + 1 ))10¹²

           v2 = 40000 + 2,059

           v = 200.005 m / s

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