Question

what is the length of the x - component of the vector shown below?
a. 23.6
b. 8.1
c. 34.1
d. 72.5

Explanation:

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

The formula for the x - component of a vector \( \vec{A} \) with magnitude \( A \) and angle \( \theta \) with the x - axis is \( A_x=A\cos\theta \). Here, \( A = 25 \) and \( \theta=71^{\circ} \).

Step2: Calculate the x - component

We know that \( \cos(71^{\circ})\approx0.3256 \). Then \( A_x = 25\times\cos(71^{\circ}) \). Substitute the value of \( \cos(71^{\circ}) \): \( A_x=25\times0.3256 = 8.14\approx8.1 \)

Answer:

B. 8.1