Question

Dynamics Question!

At the instant illustrated, car 8 has a speed of 27 km/h and car A has a speed of 35 km/h. longitudinal axis fixed to car B as indicated in the figure. relative to a 42U 310 61 m 89 m

Answer 1

Given: V_B = 27 km/h = 7.5 m/s V_A = 35 km/h = 9.722 m/s Solution Consider Delta OAB, law of cosines AB^2 = OA^2 + OB^2 - 2(OA)(OB) cos (42 + 31 = (61)^2 + (89)^2 - 2(61)(89) cos (73) r = AB = 84.3m Apply law of sines, 84.3/sin 73 degree = 61/ sin alpha = 89/sin Phi alpha = 43.8 degree Phi = 90 degree alpha +phi = 90 degree Implies Theta = 46.2 degree alpha + 31 degree + theta +beta = 180 degree beta = 51 degree V_B^vector = V_B cos beta i^vector +V_B sin beta j^vector = 7.5 cos 51 degree i^vector + 7.5 sin 51 j^vector V_B^vector = 4.72 i^vector + 5.83 j^vector V_A^vector = V_A^vector cos(alpha + 31 degree)i^vector - V_A sin (alpha + 31 degree) j^vector V_A^vector = 2.548 i^vector - 9.38 j^vector V_A/B^vector = V_A^vector - V_B^vector = 2.548 i^vector - 9.38 j^vector 4.72 i^vector - 5.83 j^vector