(Resolving a force when the angle is measured from the -axis) A force vector lies…

MATHEMATICS · Multi-part · ISC · Mathematics · Sets and Functions · Trigonometric functions: definitions, signs and values

Problem

(Resolving a force when the angle is measured from the

y

-axis) A force vector

\vec F

lies entirely in the

x

–

y

plane. It makes an angle of

25^{\circ}

with the positive

y

-axis, measured towards the positive

x

-axis. The

x

-component of the force is measured to be

F_x = 15\,\text{N}

. (i) Determine the

y

-component

F_y

of the force, stating its sign clearly. (ii) Hence find the magnitude

F

of the force. (iii) Express

\vec F

in unit-vector notation

\bigl(\,F_x\hat i + F_y\hat j\,\bigr)\,\text{N}