Question

A huge cannon is assembled on an airless planet. The planet has a radius of 5.0×106m and a mass of 2.6×1024kg . The cannon fires a projectile straight up at 3600 m/s .

Answer 1

The height the projectile reach above the surface, given that it was projected with a velocity of 3600 m/s is
`9.34*10^5\ m`

How to calculate the height the project will reach above the surface?

First, we shall calculate the acceleration due to gravity of the planet. Details below:

• Radius of planet (r) =
  `5.0*10^(6)\ m`
• Mass of planet (M) =
  `2.6*10^(24)\ Kg`
• Gravitational constant (G) =
  `6.67*10^(-11)\ Nm^(2)/Kg^(2)`
• Acceleration due to gravity of planet (g) = ?

`g = (GM)/(r^2) \\\\ g = (6.67*10^(-11)\ *\ 2.6*10^(24))/((5.0*10^(6))^(2)) \\\\g = 6.94\ m/s^2`

Finally, we shall calculate the height reach by the projectile above the surface. This is shown below:

• Initial velocity of projectile (u) = 3600 m/s
• Acceleration due to gravity of planet (g) = 6.94 m/s²
• Maximum height (h) =?

`h = (u^2)/(2g) \\\\h = (3600^2)/(2\ *\ 6.94)\\\\h = 9.34*10^5\ m`

Complete question:

A huge cannon is assembled on an airless planet. The planet has a radius of 5.0×106m and a mass of 2.6×1024kg . The cannon fires a projectile straight up at 3600 m/s. What height does the projectile reach above the surface?