# vector problem

• Dec 29th 2011, 11:41 PM
arangu1508
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.
• Dec 29th 2011, 11:53 PM
MarkFL
Re: vector problem
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?
• Dec 30th 2011, 12:04 AM
arangu1508
Re: vector problem
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
• Dec 30th 2011, 12:14 AM
MarkFL
Re: vector problem
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 $\displaystyle v_x$:

$\displaystyle \sin$$30^{\circ}$$=\frac{v_x}{10}$ solve for $\displaystyle v_x$

To find the y-component $\displaystyle v_y$:

$\displaystyle \cos$$30^{\circ}$$=\frac{v_y}{10}$ solve for $\displaystyle v_y$