Two athletes are pulling on a ring. One athlete pulls with a force of 150 N in

a northerly direction. The second athlete pulls with a force of 200 N in a
westerly direction. Calculate the magnitude [5 marks] and direction (relative
to west) [5 marks] of the resultant of these two forces?

(0,150) + (-200,0) = (-200,150)

= 250N at W 36.9°N

To calculate the magnitude and direction of the resultant force, we can use the concept of vector addition. We can represent the forces as vectors and then find the resultant vector by adding them.

Step 1: Draw a diagram
Draw a diagram representing the forces. Assume the north direction is upwards and the west direction is to the left.

Step 2: Assign a coordinate system
Assign a coordinate system to the diagram. Let the x-axis represent west and the y-axis represent north.

Step 3: Determine the components
Convert the forces into their x and y components.

The first athlete's force (150 N) is in the north direction, so its y-component is 150 N, and its x-component is 0 N.

The second athlete's force (200 N) is in the west direction, so its x-component is -200 N, and its y-component is 0 N.

Step 4: Add the components
Add the x-components and y-components separately to find the resultant force.

The x-component of the resultant force = 0 N + (-200 N) = -200 N
The y-component of the resultant force = 150 N + 0 N = 150 N

Step 5: Calculate the magnitude
Calculate the magnitude of the resultant force using the Pythagorean theorem.

Magnitude of the resultant force = sqrt((-200 N)^2 + (150 N)^2) ≈ 250 N

Step 6: Calculate the direction
Calculate the direction of the resultant force using trigonometry.

Tan(angle) = (y-component of resultant force)/(x-component of resultant force)
Tan(angle) = 150 N / (-200 N) ≈ -0.75

Angle = arctan(-0.75) ≈ -36.87 degrees

Since the x-component is negative, the angle is in the fourth quadrant, relative to west.

Therefore, the magnitude of the resultant force is approximately 250 N, and the direction, relative to west, is approximately 36.87 degrees in the fourth quadrant.

To calculate the magnitude and direction of the resultant force, we can use vector addition.

Step 1: Represent the given forces as vectors.
The first athlete pulls with a force of 150 N in a northerly direction. This can be represented by a vector pointing north with a magnitude of 150 N.
The second athlete pulls with a force of 200 N in a westerly direction. This can be represented by a vector pointing west with a magnitude of 200 N.

Step 2: Add the vectors together.
To add the vectors, we can use the head-to-tail method. Draw the vector representing the first force, and then draw the vector representing the second force, starting from the tip of the first vector. The resultant vector connects the tail of the first vector to the tip of the second vector.

Step 3: Measure the magnitude of the resultant vector.
To measure the magnitude of the resultant vector, we can use the Pythagorean theorem. The magnitude of the resultant vector is the square root of the sum of the squares of the individual vector magnitudes. In this case, the magnitude of the resultant vector is √(150^2 + 200^2) = √(22500 + 40000) = √62500 = 250 N.

Step 4: Determine the direction of the resultant vector.
To determine the direction of the resultant vector relative to the west direction, we can use trigonometry. The angle (θ) can be found by taking the inverse tangent of the ratio of the y-component of the resultant vector to the x-component of the resultant vector. In this case, θ = tan^(-1)(150/200) = tan^(-1)(0.75) = 36.87°.

Therefore, the magnitude of the resultant force is 250 N, and the direction of the resultant force relative to the west is 36.87°.