"An object is displaced 25km south-east and then 40km North direction 30 degrees North of East. Find the angle in degrees that the displaced vector makes with east."
Is it 12 degrees?
2007-09-06 09:32:52 · 3 answers · asked by Kayla G 1 in Science & Mathematics ➔ Physics
No, it is 2.54 degrees. I converted both numbers from polar to rectangular (polar numbers have a magnitude and a direction while rectangular numbers have X and Y components). Then I added the X and Y components.
Y1 = 25*SIN 45 = -17.68 and X1 = 25*COS 45 = 17.68
Y2 = 40*SIN 30 = 20 and X2 = 40*COS 30 = 34.64
Y = 2.32 and X = 52.32
Now take arctan of Y/X to put the number back into polar form (the formula for the magnitude is (X^2+Y^2)^0.5 but that wasn't part of the question). ARCTAN (Y/X = 2.32/52.32 = 0.044) = 2.54 degrees. This solution requires East be placed at 0 degrees.
2007-09-06 10:28:09 · answer #1 · answered by Amphibolite 7 · 0⤊ 0⤋
we could mark east as +x course and west as -x course. initially driving force is on the commencing place. using this convention, first he strikes a vector +8km and then -3 km vector and ultimately +12 km then addition of those vectors Vector R= vectorx1 + vector2 + vectorx3 Vector R=(+8) + (-3) + (+12) Vector R=+17 we could convert it to vector returned +x east course so he strikes 17 km in east course as displacement take care
2016-11-14 09:08:41 · answer #2 · answered by jannelle 4 · 0⤊ 0⤋
No, it's 55.6 , using MATLAB as below:
25*(cos(pi/4)+i*sin(pi/4))+60*(cos(pi/3)+i*sin(pi/3))=47.6777 +69.6392i
atan(69.6392/47.6777)= 0.9704 radian=55.6 degree
2007-09-06 09:59:49 · answer #3 · answered by Nima J 4 · 0⤊ 0⤋