Question

At the instant shown, cars A and B are traveling at velocities of

50 m/s and 30 m/s , respectively. B is increasing its velocity by 2 m/s2, while A maintains a constant velocity. The radius of curvature at B is B = 200 m.

Determine the magnitude of the velocity of B with respect to A.

Determine the direction angle of the velocity of B with respect to A.

Determine the magnitude of the acceleration of B with respect to A.

Determine the direction angle of the acceleration of B with respect to A.

Answer 1

Here, Vb/a = Vb - Va

           = -30sin30 i + 30cos30 j - 50 j

            = - 15 i - 24.019 j   m/sec

=>   magnitude of the velocity of B with respect to A = sqrt (15² + 24.019²)

                                                                                    = 28.318 m/sec

=> direction angle of the velocity of B with respect to A = 180 + tan^-1(24.019/15)

                                                                                         = 238.015   degrees   ---anticlockwise from + ve x axis

Here, centripedal acceleration = 30 *30/200

                                                    = 4.5 m/sec²

Here, Ab/a = Ab - Aa

                     = (-2sin30 - 4.5cos30) i + (2cos30 - 4.5sin30) j

                      = - 4.897 i - 0.5179 j

=>   magnitude of the acceleration of B with respect to A = 4.924 m/sec²

=>   direction angle of the acceleration of B with respect to A = 180 + tan^-1(0.5179/4.897)

                                                                                             = 186.037   degrees   ---anticlockwise from + ve x axis