Question

what is the y component of the vector in the diagram? 95n, south 60n, south 60n, north 104n, north

Explanation:

Step1: Determine the formula for the y - component

The formula for the y - component of a vector \( \vec{A} \) with magnitude \( A \) and angle \( \theta \) with the x - axis is \( A_y=-A\sin\theta\) (negative because the vector is in the fourth quadrant, south - direction in this context).

Step2: Identify the magnitude and angle

Assume the magnitude of the vector \( A = 100N\) (since the x - component \(A_x = 80N\) and using \(A_x=A\cos\theta\), \(\cos\theta=\frac{A_x}{A}\), if \(A_x = 80\) and assume \(A = 100\), \(\cos\theta=\frac{80}{100}=0.8\), then \(\theta = 37^{\circ}\))

Step3: Calculate the y - component

Using \(A_y=-A\sin\theta\), with \(A = 100N\) and \(\theta = 37^{\circ}\), \(\sin37^{\circ}\approx0.6\). So \(A_y=- 100\times0.6=-60N\), the negative sign indicates the south - direction.

Answer:

60N, south