The case of the flying Fred  
July 22, 2002 Reprinted from: 

Design
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After making several simplifying assumptions, it is determined that the speed prior to braking was about 50 mph, perhaps less than you might have guessed.


Did you ever wonder what it would be like to try a stunt like Evel Knievel, jumping a motorcycle over the Grand Canyon or a string of cars? Fred found out, but he didn't get to enjoy it very long. Fred was headed West on a rural paved road late at night after having several drinks too many. Either not seeing or ignoring the stop sign, he went right through the intersection. The gravel road straight ahead was a downward slope, which would have caused control problems even without the gravel surface. Fred lost control of his flatbed pickup, running off the road to the right into a ditch and up an embankment. He braked about 27 ft prior to hitting the embankment, going up and over and becoming airborne as he left the top. The embankment imparted a slight rotational velocity to the pickup. After traveling 40 ft, the truck was inclined at about 32° when the driver's side door hit a 12inchdiameter wooden power pole and was knocked off. The pole was broken in two places. The pickup continued airborne for another 30 ft prior to hitting a 5inchdiameter pecan tree, shearing it off. It was then airborne for another 30 ft prior to hitting the ground on a level 4.2 ft below the embankment, tumbling for another 46 ft prior to coming to rest. Fred had massive injuries and did not survive. We would like to know his speed prior to braking. This is obviously a complex situation not allowing a detailed solution here, but it is interesting to outline a method that can be used to solve this problem. The airborne freefall of a vehicle may be analyzed in many cases by considering the vehicle to be a point mass, and using the equations for ballistic trajectories given here: X = V_{0} Cos0t and Y = h + V_{0 }Sin0t  0.5 g t^{2} X and Y are the horizontal and vertical coordinates, U is the angle of departure, V_{0} is the initial velocity, h is the initial vertical position, g is the gravitational constant, and t is the time. In order to solve the trajectory equations, it is usually necessary to estimate one of the variables, usually the initial angle of the velocity vector. Since an estimate of the minimum speed may be obtained by using 45° for the initial angle, this is often done. In this case there are three such trajectories interrupted by impacts with the pole and the tree. This suggests that the problem could be analyzed in segments by working backwards as outlined below:


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