Tom, Dick and Harry are all pulling on a loop.Tom pulls North with a force of 90N and Dick pulls East with a force of 120N.

It seems like you're asking for the resultant force when Tom and Dick are pulling the loop. To find this, we can use the Pythagorean theorem because the forces are at right angles to each other.

Step 1: Square the magnitudes of each force.

• Tom's force (North): 90N^2 = 8100 N^2
• Dick's force (East): 120N^2 = 14400 N^2

Step 2: Add the squared magnitudes together.

• 8100 N^2 + 14400 N^2 = 22500 N^2

Step 3: Take the square root of the sum to find the magnitude of the resultant force.

• sqrt(22500 N^2) = 150N

So, the resultant force when Tom and Dick pull the loop is 150N. However, this is just the magnitude. The direction of the force can be found using trigonometry.

Step 4: Find the angle of the resultant force.

• We can use the tangent function for this: tan(θ) = Opposite/Adjacent
• In this case, the opposite side is Dick's force (East, 120N) and the adjacent side is Tom's force (North, 90N).
• So, tan(θ) = 120N/90N = 1.33
• To find the angle θ, we take the inverse tangent (arctan) of 1.33, which is approximately 53 degrees.

Therefore, the resultant force is 150N at an angle of 53 degrees from Tom's force (North).