Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 122

Pittsburgh left. Drivers in Pittsburgh, Pennsylvania, are alert for an aggressive maneuver dubbed the Pittsburgh left. Figure 4.39 gives an example that resulted in a collision. Cars A and B were initially stopped at a red light. At the onset of the green light at time \( t = 0 \), car A moved forward with acceleration \( a_A \) but the driver of car B, wanting to make a left turn in front of A, anticipated the light change by moving during the yellow light for the perpendicular traffic. The driver started at time \( t = -\Delta t \) and moved through a quarter circle with tangential acceleration \( a_B \) until there was a front-side collision. In your investigation of the accident, you find that the width of each lane is \( w = 3.00 \text{ m} \) and the width of car B is \( b = 1.50 \text{ m} \). The cars were in the middle of a lane initially and in the collision. Assume the accelerations were \( a_A = 3.00 \text{ m/s}^2 \) and \( a_B = 4.00 \text{ m/s}^2 \) (which is aggressive). When the collision occurred, (a) how far had A moved, (b) what was the speed of A, (c) what was the time, (d) how far had the middle front of B moved, and (e) what was the speed of B? (e) [sic, (f)] What was the value of \( \Delta t \)?