Question

Suppose that you have a miniature rocket in 3-Dimensional free space without any gravity. The rocket weighs 1 Kg, and has an engine which produces trust in Newtons in the positive x-direction. The rocket is initially at rest. Find the minimum energy in terms of the 2-norm to move the rocket 10 meters to the right, and come to rest at the new position in 10 seconds.2. Plot the thrust of the engine as a function of time

Answer 1

Part 1

As given by the problem, the rocket has to cover a distance of 10meters in 10seconds.

Thus, velocity is given by

Hence we get velocity as 1m/s.

We know, Kinetic energy =

Now, m= 1kg and v= 1m/s,

Therefore, Kinetic energy = (1/2)*1kg*1m²/s² = 0.5Joule.

Part 2

When the rocket covers a distance "L" due to a force "F" acting on it,

Then, the energy is given by, Energy= Force * Distance

From which we get, Force= = =0.05N.