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