Excellent job except for one small oversight. See my note.
Sir,
The question states, Find a vector whose Magnitude is 4.9 and whose component in the x direction is .686 times its component in the y direction,
Answer..
x=(.686 *y) Therefore, Magnitude of vector (v) = Sqrt (x^2+y^2) =4.9
So, Sqrt((.686y)^2 + y^2) = 4.9
(.686y)^2 + y^2)=(4.9)^2
y^2(1+.686) =(4.9)^2
The .686 was part of a term that was squared.
(.686y)^2 + y^2)=(4.9)^2 gives you
.686^2 y^2 + y^2 = 4.9^2 wo you would have
y^2(1+.686^2) =(4.9)^2.
This would change your solution for y somewhat; the resulting answer should then give you results that check out.
y^2 =((4.9)^2)/(1+.686)
y^2= 14.241 therefore y= 3.774
If x=.686 *y then x= .686*3.774 Therefore x= 2.589
I would have said v= 2.589i + 3.774j was my vector, but the sqrt(x^2+y^2) does not equal 4.9 rather 4.57
So I've done something wrong..
Can you clarify...
You caught the error. However you didn't copy down the new y component correctly when you checked your result:
y^2= 16.32 therefore y= 4.04
If x=.686 *y then x= .686*4.04 Therefore x= 2.771
I would have said v= 2.771i + 3.774j
Shouldn't this be v = 2.771 i + 4.04 j? Looks like this will just about exactly fix the discrepancy.
was my vector, but the sqrt(x^2+y^2) does not equal 4.9 rather 4.68