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Question: in this problem well analyze a car collision assume that...

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In this problem well analyze a car collision. Assume that both Car A and B are initially traveling to the right at 95 ft/s. Car A is tailgating, leaving very little room between the front (F) of his car and the rear (R) of car B. In spite of this, the driver in car A starts fiddling with the radio and stops paying attention to Car B. At this instant, the driver in Car B notices an accident ahead of him and starts to brake, causing a deceleration of 19 ft/s2. By the time the driver of Car A looks up, the gap between the two cars has narrowed to 24 ft and the speed of Car B has dropped to 67 ft/s. Assume that the driver of Car A immediately reacts and tries to apply maximum braking. The driver of Car A has good reflexes and it therefore only takes 0.5 s for him to hit the brakes. Assume that his car has better brakes than the one in front and that his car begins to decelerate at 21 r/s2 upon contact with the brake pedal (at t 0.5 s). Calculate when the collision occurs and the relative speed of the collision. Lets begin by calculating the positions and speeds of the two cars when the driver of Car A hits the brake pedal at t- 0.5 s. For convenience, let XAF 0 ft at t- 0 s, where XAF refers to the front of Car A. Let XBR refer to the rear of Car B. CalculaAF.5 s), XBR(0.5 s), VA(0.5 s) and B(0.5 s), the latter two quantities being the speeds of Cars A and B, respectively. XAF(0.5 s) = KgR(0.5 s) = VA(0.5 s) = B(0.5 s) ft ft ft/s ft/s

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