Question

A vector is inclined at an angle 60∘ to the horizontal. If its rectangular component in the horizontal direction is 50 N, then its magnitude in the vertical direction is

A. 25 N

B. 75 N

C. 87 N

D. 100 N

Answer 1

The vertical component of a vector inclined at 60 degrees with a horizontal component of 50 N is found using the sine function. The vertical component is approximately 87 N, corresponding to option C.

Step-by-step explanation:

The student asked about the vertical component of a force vector that is inclined at an angle of 60 degrees to the horizontal. Given that the horizontal component is 50 N, we can use trigonometric functions to find the vertical component. Specifically, we use the sine function because sine relates the opposite side to the hypotenuse in a right-angled triangle, and in this scenario, the vertical component is the opposite side to the angle given.

To calculate the magnitude of the vertical component (Fy), we have:

• Fx / F = cos(60°) (Fx is the horizontal component and F is the magnitude of the vector)
• 50 N / F = 1/2 (since cos(60°) = 1/2)
• F = 50 N / (1/2) = 100 N (total magnitude of the vector)
• Fy = F * sin(60°) = 100 N * (√3/2)
• Fy = 50√3 N which approximately equals 86.6 N.

Therefore, the correct answer for the vertical component's magnitude is approximately 87 N, which corresponds to option C.