Question

1. Two points in a plane have polar coordinates (2.5 m, 30 degrees) and (3.8 m, 120 deg). Determine (a) the cartesian coordinates of both points and (b) the distance between the points.

2. Vector A has magnitude 29 units and points along +y. When vector B is added to the vector A, the resultant ponits along -x with a magnitude of 14 units. Find the magnitude and directions of B.

3. Repeat #2, for the same vector A, but for the case where the resultant of A and B points along -y with a magnitude of 14 units .

Answer 1

1a. 2.5m[30o]
X = 2.5*cos30 = 2.17 m.
Y = 2.5*sin30 = 1.25 m.
P1(2.17,1.25).

3.8m[120o]
X = 3.8*cos120 = -1.9 m.
Y = 3.8*sin120 = 3.29 m.
P2(-1.9,3.29).

1b. (2.17,1.25), (-1.9,3.29)

d^2=(-1.9-2.17)^2 + (3.29-1.25)^2= 20.73
d = 4.55 m.

2. A + B = -14
29i + B = -14
B = -14 -29i = 32.2[244.2o]

3. A + B = -14i
29i + B = -14i
B = -43i = 43[270o].