Thread: vector problem

Kindly guide me in the following vector problem:

Magnitude of a velocity vector is 10 m/s. If theta = 30 degrees, find its (i) x component (ii) y component. Theta is measured from +ve side of the y-axis. Hope I have made myself clear.

Thanks for the help.

Draw a sketch. Draw your x and y axes, draw the vector originating from the origin and 30° less than vertical. Label the angle. From the terminus of the vector draw a horizontal line segment to the y-axis. This segment is your x-component and the length along the y-axis from the origin to the point where the horizontal segment meets the y-axis is your y-component.

The magnitude of the vector is the hypotenuse, how do you find length of the legs, i.e., the x and y components?

cos 30 = opp/10 ; sin 30 = adj/10; cos 30 = sq.root of 3 /2 and sin 30 = 1/2 ;

Is the method correct?

Thank u

You have the definitions of sine and cosine reversed, but you are on the right track. What is probably throwing is that usually the angles are measured from the positive x-axis in a counter-clockwise motion. The angle in this problem is measured from the positive y-axis, where I am assuming in a clockwise motion. If that's not the case, then we just reverse the sign of the x-component.

To find the x-component :

solve for

To find the y-component :

solve for