A forse of 75 N due north and 105 N due east is acting on a point. What is the magnitude and direction of the resultant force? What is the magnitde and direction of the equilibrant?

To find the magnitude and direction of the resultant force, we need to use vector addition. We can add the north and east forces together like adding two vectors to find the resultant.

Step 1: Draw a diagram to represent the forces. Let's assume that north is the positive y-axis and east is the positive x-axis.

Step 2: Break down the forces into their x and y components. The north force of 75 N is acting only in the y-axis (upwards), and the east force of 105 N is acting only in the x-axis (rightwards).

North force component: 75 N in the positive y-axis direction.
East force component: 105 N in the positive x-axis direction.

Step 3: Add the components of the forces together. Since the forces are acting at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant force.

Resultant force magnitude (R) = √[(North force component)^2 + (East force component)^2]
R = √[(75 N)^2 + (105 N)^2]
R = √[5625 N^2 + 11025 N^2]
R = √16650 N^2
R = 129 N (approximately, rounded to the nearest whole number)

Step 4: Find the direction of the resultant force. We can use trigonometry to find the angle.

Resultant force angle (θ) = arctan(North force component / East force component)
θ = arctan(75 N / 105 N)
θ = arctan(0.7143)
θ = 36.8 degrees (approximately, rounded to one decimal place)

Therefore, the magnitude of the resultant force is approximately 129 N, and it is directed at an angle of 36.8 degrees with respect to the positive x-axis.

To find the magnitude and direction of the equilibrant, we need to find a force that will balance out the resultant force. The equilibrant has the same magnitude as the resultant force, but its direction is the exact opposite.

Magnitude of the equilibrant = Magnitude of the resultant force = 129 N

Direction of the equilibrant = Direction of the resultant force + 180 degrees
Direction of the equilibrant = 36.8 degrees + 180 degrees
Direction of the equilibrant = 216.8 degrees (approximately, rounded to one decimal place)

Therefore, the magnitude of the equilibrant is approximately 129 N, and it is directed at an angle of 216.8 degrees with respect to the positive x-axis.

To find the magnitude and direction of the resultant force, we need to use vector addition. We can represent the North force of 75 N as a vector of magnitude 75 N pointing directly north, and the East force of 105 N as a vector of magnitude 105 N pointing directly east.

We can then draw a diagram or use trigonometry to find the resultant force:

Step 1: Draw a diagram with the north force (75 N) and east force (105 N) as vectors originating from the same point.

Step 2: Use the Pythagorean theorem to find the magnitude of the resultant force. The magnitude of the resultant force (R) can be found using the formula R = √(A^2 + B^2), where A is the north force and B is the east force.

R = √(75^2 + 105^2) = √(5625 + 11025) = √16650 ≈ 129 N

Step 3: Use trigonometry to find the direction of the resultant force. The angle θ between the resultant force and the north direction can be found using the formula θ = arctan(B/A), where A is the north force and B is the east force.

θ = arctan(105/75) ≈ 55.1 degrees

Therefore, the magnitude of the resultant force is approximately 129 N, and its direction is approximately 55.1 degrees East of North.

To find the magnitude and direction of the equilibrant force, we need to find a force that will balance the original forces. The magnitude of the equilibrant force will be equal in magnitude but opposite in direction to the resultant force.

Magnitude of the equilibrant force = 129 N
Direction of the equilibrant force = 180 degrees + 55.1 degrees ≈ 235.1 degrees

Therefore, the magnitude of the equilibrant force is approximately 129 N, and its direction is approximately 235.1 degrees.