1. To demonstrate the tremendous acceleration of a top fuel drag racer, you attempt to run your car into the back of a dragster that is "burning out" at the red light before the start of a race. (Burning out means spinning the tires at high speed to heat the tread and make the rubber sticky.) You drive at a constant speed of v,, toward the stopped dragster, not slowing down in the face of the imminent collision. The dragster dn'ver sees you coming but waits until the last instant to put down the hammer, accelerating from the starting line at constant acceleration a,. Let the time at which the dragster starts to accelerate be t=0. Make a sketch of the situation and answer the following (make sure to explain your reasoning a little, notjust a \"mumblejumble" of equations or worse yet ofjust numbers}: a] What is lmax, the longest time after the dragster begins to accelerate that you can possibly run into the back of the dragster if you continue at your initial velocity? b] Assuming that the dragster has started at the last instant possible (so your front bumper almost hits the rear of the dragster at t= lmax). nd your distance from the dragster when he started. If you calculate positions on the way to this solution, choose coordinates so that the position of the drag car is 0 at t=0. Rememberthat you are solving for a distance {which is a magnitude, and can never be negative}, not a position (which can be negative}. 2. A car is moving at a constant velocity next to and parallel to railroad tracks. When its frontjust reaches the rear of a 92 m long train, the train starts accelerating from rest at a constant rate. After 14 seconds, the front of the car just reaches the front of the train, but after 28 seconds, the car has fallen back to the rear of the train. Make a [correctH] sketch of the situation. From this information, calculate the velocity of the car and the acceleration of the train. 3. The position of a projectile as a function of time is given by the usual equation: which can be written in x- and y-components {the X-axis should be considered as the horizontal axis in what follows]. But, since gravity is the only force acting on a projectile, and since the gravitational force is directed vertically downwards, the acceleration has no x-component. You may further assume that the y-component of the acceleration is (the sign depends on the choice of the Y-axis of course, \"shadows\" of vectors are signed numberslj. Using this equation then, calculate the following note that the result should be containing vector components instead of the launching angle that you usually see in books: a] How long does it take for a projectile to fall back to the same height as it was launched from? b] When it reaches its launching level, how far is it away from the launching point? c] And perhaps with a little bit of extra thinking and some more "evolution equations" [not guessing!], you can find the time the projectile needs to reach its maximum height above launching level AS WELL AS the maximum height above launching level itself? Tryr itll