A certain vector has a magnitude of 23 and a direction of \( 202^{\circ} \) What is the vertical component of this vector? Round your answer to 3 decimal places.

To find the vertical component of a vector, you can use the sine function. The vertical component \( V_y \) is calculated as: \[ V_y = V \cdot \sin(\theta) \] where \( V \) is the magnitude of the vector and \( \theta \) is the angle in degrees. Given: - Magnitude \( V = 23 \) - Angle \( \theta = 202^{\circ} \) Calculating the vertical component: \[ V_y = 23 \cdot \sin(202^{\circ}) \] Using a calculator: \[ V_y \approx 23 \cdot (-0.978) \approx -22.494 \] So, the vertical component rounded to three decimal places is: **-22.494**.