Answer:
hat the speed of the rocket is lower than the minimum escape velocity whereby the ship cannot escape the planet
Explanation:
To find out if the projectile can escape the planet, let's find the minimum escape velocity using the concepts of energy.
Starting point. On the planet's surface
Em∠₀ = k + U = ½ m v² - G mM / R²
End point far away
Emf = U = - g m M / r²
Em₀ = Emf
½ m v² - G m M / R² = -G m M / r²
v² = G M (1 / R² -1 / r²)
Let's find the velocity for the height of the rocket r = 4R
v =√GM (1 / R² - 1/16 R²) = √a GM / R² 0.968
This is the speed to escape planet
Let's compare this minimum escape velocity with the given value
v = √GM /R² 1 /√ 3
v = √GM / R 0.577
We can see that the speed of the rocket is lower than the minimum escape velocity whereby the ship cannot escape the planet
