Answer:
3.6×10⁶ m
Explanation:
Newton's law of universal gravitation states that the force between two masses is:
F = GMm / r²
where G is the universal constant of gravitation (6.67×10⁻¹¹ m³/kg/s²),
M is the mass of one object
m is the mass of the other object,
and r is the distance between the center of masses of the objects.
The force acting on the meteor is:
∑F = ma
GMm / r² = ma
GM / r² = a
Given M = 6×10²⁴ kg and a = 4 m/s²:
(6.67×10⁻¹¹ m³/kg/s²) (6×10²⁴ kg) / r² = 4 m/s²
r = 10⁷ m
The distance from the meteor to the center of the Earth is 10⁷ m. We want to know what the height of the meteor is (distance to the surface of the Earth). So we need to subtract the Earth's radius.
h = 10⁷ m − 6.4×10⁶ m
h = 3.6×10⁶ m
