1. Two forces ř = (8t + 3j )N and F, = (4i + 6j )N are acting on an object. What is the

Question

magnitude and direction of the resultant force?

Answer 1

To find the magnitude and direction of the resultant force, we can add the two forces vectorially.

Adding the x-components:
8t + 4 = 12t

Adding the y-components:
3 + 6 = 9

Therefore, the resultant force is given by Fr = (12t)i + 9j N.

To find the magnitude of the resultant force, we can use the Pythagorean theorem:

|Fr| = sqrt((12t)^2 + 9^2)
|Fr| = sqrt(144t^2 + 81)

The direction of the resultant force can be found using the arctan function:

θ = arctan(9/(12t))

So, the magnitude of the resultant force is sqrt(144t^2 + 81) and the direction is θ = arctan(9/(12t)).