A 12,500 N alien UFO is hovering about the surface of Earth. At time , its position can be given as () = ((0.24 m/s^3)^3 + 25 m)i^ ((4.2 m/s))j^+ (−(0.43 m/s^3)^3 + (0.8 m/s^2)^2)k^. What is the net force acting on the UFO at time = 2 s? Express your answer in vector format. What is its magnitude?

a)

b) 5843 N

Explanation:

a)

The position of the UFO at time t is given by the vector:

Therefore it has 3 components:

We start by finding the velocity of the UFO, which is given by the derivative of the position:

And then, by differentiating again, we find the acceleration:

The weight of the UFO is W = 12,500 N, so its mass is:

Therefore, the components of the force on the UFO are given by Newton's second law:

So, Substituting t = 2 s, we find:

So the net force on the UFO at t = 2 s is

b)

The magnitude of a 3-dimensional vector is given by

where

are the three components of the vector

In this problem, the three components of the net force are:

Therefore, substituting into the equation, we find the magnitude of the net force: