Question

In the  23^rd century, an Earth probe to the planet Altair IV (mass 3.5x10²⁴ kg, radius 5.08x10⁶ m) has a communications failure. To request assistance, a small projectile is shot toward Earth from the surface of the planet, at speed 18x10³ m/s (which is greater than the escape speed). Ignore friction and all other objects in the universe, and assume the projectile has no fuel. Find the speed of the projectile, in m/s, when it reaches Earth, which is far enough from Altair IV so the planet has negligible gravitational pull on the projectile (at r = ∞). Give your answer in scientific notation.

Answer 1

From energy conservation principle the energy and surface of the planet Altair would be equal to the energy at surface of earth. We use this to find the required speed at the surface of earth as shown below