Question

what is the length of the x - component of the vector shown below?
a. 7.1
b. 30.0
c. 8.6
d. 5.5

Explanation:

Step1: Use the formula for the x - component of a vector

The formula for the x - component of a vector \( \vec{A} \) with magnitude \( |\vec{A}| \) and angle \( \theta \) with the x - axis is \( A_x=|\vec{A}|\cos\theta \). Here, \( |\vec{A}| = 9 \) and \( \theta = 38^{\circ} \).

Step2: Calculate the value

We know that \( \cos(38^{\circ})\approx0.788 \). Then \( A_x = 9\times\cos(38^{\circ}) \). Substitute \( \cos(38^{\circ})\approx0.788 \) into the formula: \( A_x=9\times0.788 = 7.092\approx7.1 \).

Answer:

A. 7.1