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

`1.67* 10^6 m`

Step-by-step explanation:

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

`g=(GM)/(R^2)`

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

`g=(6.67* 10^(-11) * 3.52* 10^(24))/((5.40* 10^6)^2) = 8.05 N/kg`

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

`h=(v^2)/(2g)\\h = (5180^2)/(2* 8.05) =1.67* 10^6 m`