Scientists are developing a new space cannon to shoot objects from the surface of the Earth directly 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 aconstant gravitational deceleration of 9.81 m/s2. (b) considering the change of the gravitational force with height. Note: Neglecttheairresistanceforthisproblem. Use6.67×10−11 m3kg−1s−2 forthegravitational constant, 6371 km for the Earth’s radius, and 5.97 × 1024 kg for the Earth’s mass.
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