To review the solution to a similar problem, consult Interactive Solution 1.43. The magnitude of a force vector is 87.4 newtons (N). The x component of this vector is directed along the x axis and has a magnitude of 72.1 N. The y component points along the y axis. (a) Find the angle between and the x axis. (b) Find the component of along the y axis.

(a) 34.4°

(b) 49.4 N

Explanation:

(a) From the diagram,

Amgle between the x axis can be calculated as,

cosΘ = adjacent/hypoteneous

cosΘ = 72.1/87.4

cosΘ = 0.8249

Θ = cos⁻¹(0.8249)

Θ = 34.4°.

Hence the angle between the x axis is 34.4°

(b) To find the component along the y axis we make use of pythagoras theorem.

a² = b²+c²................... Equation 1

Where a = 87.4 N, b = 72.1 N, c = y.

Substitute  these values into equation 1

87.4² = 72.1² + y²

y² = 87.4²-72.1²

y² = 2440.35

y = √(2440.35)

y = 49.4 N