Question

The magnitude of a force vector is 89.6 newtons (N). The x component of this vector is directed along the +x axis and has a magnitude of 74.4 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.

Answer 1

(a) θ = 33.86°

(b) Ay = 49.92 N

Step-by-step explanation:

You have that the magnitude of a vector is A = 89.6 N

The x component of such a vector is Ax = 74.4 N

(a) To find the angle between the vector and the x axis you use the following formula for the calculation of the x component of a vector:

`A_x=Acos\theta` (1)

Ax: x component of vector A

A: magnitude of vector A

θ: angle between vector A and the x axis

You solve the equation (1) for θ, by using the inverse of cosine function:

`\theta=cos^(-1)((A_x)/(A))=cos{-1}((74.4N)/(89.6N))\\\\\theta=33.86\°`

the angle between the A vector and the x axis is 33.86°

(b) The y component of the vector is given by:

`A_y=Asin\theta\\\\A_y=(89.6N)sin(33.86\°)=49.92N`

the y comonent of the vecor is Ay = 49.92 N