Question

1. a surfer is catching a wave. the diagram shows that it is 43.0 meters long and is 26.5° south of west. how long is the western component of the vector? no unit needed

40.8
20.4
45.8
25.7

Explanation:

Step1: Recall the formula for the horizontal component

The formula for the horizontal component \(v_x\) of a vector \(v\) with magnitude \(|v|\) and angle \(\theta\) (measured from the east - axis, here \(\theta = 28.5^{\circ}\) north of east) is \(v_x=|v|\cos\theta\).

Step2: Substitute the given values

We are given \(|v| = 43.0\) m and \(\theta = 28.5^{\circ}\). Then \(v_x = 43.0\times\cos(28.5^{\circ})\).
We know that \(\cos(28.5^{\circ})\approx0.878\).
So \(v_x=43.0\times0.878 = 37.754\approx37.8\) m.

Answer:

37.8 m