Vehicles A and B are travelling toward each other in opposing lanes on a straight segment of a two-lane highway at 35 and 40 mi/h, respectively. If the critical rates of angular change of the two drivers are 0.0065 and 0.0055 rad/s, determine (a) which driver will be first to displace laterally and (b) the longitudinal distance between vehicles when the displacement will occur. Assume that the lateral separation between the two vehicles is 6 ft.

a) From lateral displacement = 0.5wvt^2

given that VA = 35mi/hr, VB = 40mi/h

WA = 0.0065 rad/s, WB = 0.0055 rad/s

for vehicle A; Lateral displacement = 0.5 x 0.0065 x 35 x t^2 = 0.11375t^2 (mi. sec/hr0 for vehicle B; 0.5 x 0.0055 x 40 x t^2 = 0.11t^2 (mi. sec/hr) from the value gotten, it is obvious that vehicle A has a more greater lateral displacement than vehicle B

b) Equate lateral displacement of A = 14ft to get the time

0.11t^2 (mi. sec/hr) = 14

t = 9.1615secs

displacement = speed x time

= 35mi/hr x 9.1615secs + 40mi/hr x 9.1615secs = 0.2miles