Question

Find the resultant vector T = R + S when: R = 20 m; θ = 25° S = 37 m; θ = 60°

Answer 1

To calculate the resultant vector T of vectors R and S, each vector's components are determined using trigonometry, summed up, and the resultant vector's magnitude and direction are found via the Pythagorean theorem and the inverse tangent function.

Step-by-step explanation:

To find the resultant vector T = R + S when given vectors R and S, with their magnitudes and directions, one must break down each vector into its horizontal and vertical components using trigonometry, and then add the corresponding components together.

In this case, vector R has a magnitude of 20 m and a direction of 25° from the x-axis, and vector S has a magnitude of 37 m and a direction of 60° from the x-axis. By applying trigonometric functions, we can find the components of each vector:

For vector R:

• Rx = 20 m * cos(25°)
• Ry = 20 m * sin(25°)

For vector S:

• Sx = 37 m * cos(60°)
• Sy = 37 m * sin(60°)

The components are then added:

• Tx = Rx + Sx
• Ty = Ry + Sy

After calculating Tx and Ty, we can use the Pythagorean theorem to find the magnitude of the resultant vector T:

T = √(Tx² + Ty²)

Finally, to find the direction of vector T relative to the x-axis, we calculate the angle using the tangent function:

θT = atan(Ty/Tx)