Question

Consider two displacements, one of magnitude 12 m and another of magnitude 16 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 28 m, (b) 4 m, and (c) 20 m.

Answer 1

here,

magnitude of A , A = 12 m

magnitude of B , B = 16 m

let the angle between the displacements be theta

a)

the resultant , R = sqrt(A^2 + B^2 + 2 * A * B * cos(theta))

28^2 = 12^2 + 16^2 + 2 * 12 * 16 * cos(theta)

solving for theta

theta = 0 degree

the angle between the displacements is 0 degree

b)

the resultant , R = sqrt(A^2 + B^2 + 2 * A * B * cos(theta))

4^2 = 12^2 + 16^2 + 2 * 12 * 16 * cos(theta)

solving for theta

theta = 180 degree

the angle between the displacements is 180 degree

c)

the resultant , R = sqrt(A^2 + B^2 + 2 * A * B * cos(theta))

20^2 = 12^2 + 16^2 + 2 * 12 * 16 * cos(theta)

solving for theta

theta = 90 degree

the angle between the displacements is 90 degree