Question #1b250

1 Answer
Jan 18, 2017

We need to use law of parallelogram of vector addition. For two vectors vecP and vec Q having an angle theta between the two the resultant vector vecR is given by
|vecR|=sqrt(|vecP|^2+|vecQ|^2+2|vecP||vecQ|costheta)
and angle of the resultant alpha=tan^-1((|vecQ|sintheta)/(|vecP|+|vecQ|cos theta))

Inserting given values we get
|vecR|=sqrt((6000)^2+(6000)^2+2xx6000xx6000xxcos60)
=>|vecR|=sqrt((6000)^2+(6000)^2+2xx6000xx6000xx0.5)
=>|vecR|=6000sqrt3
=>|vecR|=10392.3N rounded to one decimal place.

and alpha=tan^-1((6000xxsin60)/(6000+6000cos 60))
=>alpha=tan^-1((sqrt3/2)/(1+1/2))
=>alpha=tan^-1(1/sqrt3)
=>alpha=30^@ measured as per measurement of angle theta