Question

A huge cannon is assembled on an airless planet. The planet has a radius of 5.40×106 m and a mass of 3.52×1024 kg. The cannon fires a projectile straight up at 5180 m/s. What height does the projectile reach above the surface?

Answer 1

Answer:

$1.67\times 10^6 m$

Explanation:

The gravitational acceleration on the planet can be calculated as follows:

$g=\frac{GM}{R^2}$

Where, M is the mass of the planet and R is the radius of the planet.

$g=\frac{6.67\times 10^{-11} \times 3.52\times 10^{24}}{(5.40\times 10^6)^2} = 8.05 N/kg$

The height that the projectile would reach can be calculated as follows:

$h=\frac{v^2}{2g}\\h = \frac{5180^2}{2\times 8.05} =1.67\times 10^6 m$