Question

Suppose that you have a miniature rocket in 3-dimensional free space without any gravity. The rocket

weights 1 Kg, and has an engine which produces trust in Newtons in both the positive and negative x
directions. The rocket is initially at rest. Find the minimum energy in terms of the 2-norm presented
in class to move the rocket 10 meters to the right, and come to rest at the new position in 10 seconds.

Answer 1

The minimum energy required to move the rocket 10 meters to the right and come to rest at the new position in 10 seconds is 100 Joules.

Step-by-step explanation:

To find the minimum energy required to move the rocket, we need to consider the work done by the rocket's engines. The work is equal to the force applied by the engine multiplied by the distance traveled. In this case, the force applied by the engine is equal to the thrust produced by the engine, while the distance traveled is 10 meters to the right.

Using the equation for work, W = Fd, we can calculate the minimum energy required as:

Minimum Energy = Thrust * Distance = 10 N * 10 m = 100 Nm = 100 J

So, the minimum energy required to move the rocket 10 meters to the right and come to rest at the new position in 10 seconds is 100 Joules.