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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.

User Efe
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Answer:

(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

User Aiao
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