Final answer:
The magnitude of the resultant force is 15 N and the direction is approximately 36.87 degrees from the positive x-axis, calculated using vector addition and arctangent.
Step-by-step explanation:
To calculate the magnitude and direction of the resultant force acting on the object, we must add the two given forces, F1=(8i+3j)N and F2=(4i+6j)N, using vector addition. To do this, we add the respective components:
Sum of i (x-direction) components: 8 + 4 = 12
Sum of j (y-direction) components: 3 + 6 = 9
The resultant force, F, is therefore:
F = (12i + 9j)N
The magnitude of this resultant force is given by the Pythagorean theorem:
Magnitude of F = \(\sqrt{12^2 + 9^2}\) = \(\sqrt{144 + 81}\) = \(\sqrt{225}\) = 15 N
The direction of F is measured from the positive x-axis towards the force vector. We can find the direction using the arctangent of the ratio of the j component to the i component:
Direction = \(tan^{-1}(\frac{9}{12})\)
Now, we calculate the angle:
Direction = \(tan^{-1}(\frac{3}{4})\) = 36.87 degrees
Thus, the resultant force has a magnitude of 15 N and is directed at an angle of approximately 36.87 degrees from the positive x-axis.