problem 1.7 - find the x and y components of the given 20 - lb force.

Explanation:

Step1: Calculate the magnitude of the resultant vector

We can use the Pythagorean theorem to find the magnitude of the resultant vector. The components of the vector are (x = 4) and (y = 3). The magnitude (r) of the vector with components ((x,y)) is given by (r=\sqrt{x^{2}+y^{2}}). So, (r = \sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5).

Step2: Find the x - component of the force

The x - component of the force (F_x) is given by (F_x=\frac{x}{r}F). Here, (x = 4), (r = 5) and (F=20) lb. So, (F_x=\frac{4}{5}\times20 = 16) lb.

Step3: Find the y - component of the force

The y - component of the force (F_y) is given by (F_y=\frac{y}{r}F). Here, (y = 3), (r = 5) and (F = 20) lb. So, (F_y=\frac{3}{5}\times20=12) lb.

Answer:

The x - component of the force is (16) lb and the y - component of the force is (12) lb.