Problem 2 The two trains travel on separate tracks one circu

Problem 2: The two trains travel on separate tracks, one circular and one straight. The train on the circular track is traveling at a constant speed of 50 ft/s, while the train on the straight track is traveling at a speed of 20 ft/s and its speed is increasing at a rate of 2ft/s2. What is the velocity of passenger A as observed by passenger B (i.e., in coordinate system fixed to the train car that passenger B is in)? 500 ft 50 ftls 20 ftls

Solution

vel of A = 20 ft/s

acceleration a = 2 ft/s²

distance travelled at any instant by A = s= ut + 0.5 * a * t²

                                                           = 20t + t²

angular vel of B = w = v / r

                             = 0.1 rad/s

By taking the centre of circle as reference

r_b = 500 (sin (wt) i + cos (wt) j )

r_a = 1000 i + (20t + t²) (-j)

   = 1000 i - ( 20t + t² ) j

r_b - r_a = (500sin wt + 1000) i +( 500cos wt -(20t + t²)) j

differentiating this gives velocity

v_b - v_a = (50cos wt) i + (-50sin wt - (20 + 2t)) j

          = ( 50 cos wt) i - ( 50sin wt + (20 + 2t)) j

rel velocity changes at every instant..it can be found at particular instant at time t in above eq.