Final answer:
The altitude above Earth's surface where the gravitational acceleration is 4.9 m/s^2 is approximately 1,456,190 meters.
Step-by-step explanation:
The acceleration due to gravity at a given altitude above Earth's surface can be calculated using the formula:
g = G * M / r2
Where:
- g is the acceleration due to gravity
- G is the gravitational constant (approximately 6.67430 × 10-11 m3 kg-1 s-2)
- M is the mass of Earth (approximately 5.9726 × 1024 kg)
- r is the distance from the centre of Earth
Given that the gravitational acceleration is 4.9 m/s2, we can rearrange the formula to solve for r:
r = sqrt(G * M / g)
Substituting the values, we get:
r = sqrt(6.67430 × 10-11 * 5.9726 × 1024 / 4.9)
Calculating this expression gives us:
r ≈ 1,456,190 meters
Therefore, the altitude above Earth's surface where the gravitational acceleration is 4.9 m/s2 is approximately 1,456,190 meters.