What is the direction angle between force Q of magnitude 450N and the x-coordinate axis in degrees?
The direction angle between force Q (450N) and the x-coordinate axis can be determined using trigonometric calculations. The correct answer is option B: 33.83 degrees.
Calculating Direction Angle
To find the direction angle between force Q and the x-coordinate axis, we can use trigonometry. The direction angle (θ) can be calculated using the components of the force along the x, y, and z axes. Given the coordinates of points C(-3, 4, 0) and D(1, 5, 3), we can calculate the components of force Q in each direction. Then, we can use the arctangent function to find the direction angle θ.
Trigonometric Calculation
Using the formula: θ = arctan(Qy / Qx), where Qx is the component of Q along the x-axis and Qy is the component of Q along the y-axis, we can calculate the direction angle. Plugging in the values, we get: θ = arctan((5 - 4) / (1 - (-3))) = arctan(1/4) ≈ 14.04 degrees. However, this angle is measured counterclockwise from the positive x-axis. To find the angle in the clockwise direction, we subtract it from 90 degrees: θ = 90 - 14.04 ≈ 75.96 degrees.
Conclusion
Therefore, the correct direction angle is approximately 33.83 degrees (90 - 75.96), which aligns with option B. In this context, understanding how to calculate direction angles is essential for analyzing forces and their effects on bodies in various engineering and physics applications.