Scientists are developing a new space cannon to shoot objects from the surface of the Earth di- rectly into a low orbit around the Earth. For testing purposes, a projectile is fired with an initial velocity of 2.8 km/s vertically into the sky. Calculate the height that the projectile reaches, .. (a) assuming a constant gravitational deceleration of 9.81 m/s². (b) considering the change of the gravitational force with height. Note: Neglect the air resistance for this problem. Use 6.67×1011 m³kg-'s-2 for the gravitational constant, 6371 km for the Earth's radius, and 5.97 x 1024 kg for the Earth's mass.

Scientists are developing a new space cannon to shoot objects from the surface of the Earth di- rectly into a low orbit around the Earth. For testing purposes, a projectile is fired with an initial velocity of 2.8 km/s vertically into the sky. Calculate the height that the projectile reaches, .. (a) assuming a constant gravitational deceleration of 9.81 m/s². (b) considering the change of the gravitational force with height. Note: Neglect the air resistance for this problem. Use 6.67×1011 m³kg-'s-2 for the gravitational constant, 6371 km for the Earth's radius, and 5.97 x 1024 kg for the Earth's mass.