Question

The two vectors a and
b in Fig. have equal magnitudes of 10.0 m and the angles are
37 and 106 . Find the (a) x and (b) y components of their vector sum r , (c) the magnitude of r , and (d) the angle r makes with the positive direction of the x axis

Answer 1

Explanation:

Given The two vectors a and b in Fig. have equal magnitudes of 10.0 m and the angles are 37 and 106. . Find the (a) x and (b) y components of their vector sum r , (c) the magnitude of r , and (d) the angle r makes with the positive direction of the x axis

• The x component will be the projection of vector on x axis for the vector p
• So px = p. cos theta 1
• Similarly
• So py = p sin theta 1
• Now for the vector q we have the angle between vector p and q is  
• Theta 3 = 180 – theta 2
•             = 180 – 106
•             = 74 degree
• The angle between q and x axis will be
•  180 – (theta 1 + theta 2)
•  180 – (37 + 106)
•  180 – 143
•   = 37 degrees
• The x – component of vector q will be
• So qx = q cos 37 degree
• The y – component of vector p will be
• So qy = q sin 37 degree
• The x component of vector q is in the opposite direction of the x component of vector p means x component of vector R will be
• Rx = px + qx
•      = 10 cos 37 – 10 cos 37
•     = 0
• The y component will be
• Ry = py + qy
•     = 10 (sin 37 + sin 37)
•     = 3.612 m
• Now the magnitude of R will be  
• R^2 = Rx^2 + Ry^2
• R = √0 + 3.612
• R = √3.612
• R = 1.9 m
• So angle Of  vector R will be
• So tan theta R = Ry / Rx
• So theta = arc tan (0) = 0 degree