Motion Formulae

Force

For simplicity we will say that the forces acting on the rocket are thrust and gravity. Therefore,

F_net=ma=Ru-mg

where R is the rate of fuel consumption, u is the velocity of the gasses with respect to the rocket, m is the mass of the rocket, and g is the gravitational acceleration of the earth.

Acceleration

a=F_net/m

Velocity

This equation was derived for velocity in space. We will assume that the velocity on earth is close to this.

v_f=-uln(m_f/m_i) + v₀

Momentum

Momentum is mostly used for collisions so if you want to know what would happen if a rocket hit you while it was moving...

p=mv

Escape Velocity

The escape velocity is the velocity that a ballistic projectile needs in order to break away from the Earth's gravitational pull. Its value is

v_esc=40320 km/h

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