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:
