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81.

81. Ill Careful measurements have been made of Olympic sprinters in the 100 meter dash, A simple but reasonably accurate model is that a sprinter accelerates at 3.6 mfs2 for 3% s, then runs at con- stant velocity to the finish line. a. What is the race time for a sprinter who follows this model? b. A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter's top speed is the same as in part a, what acceleration would he need to run the 100 meter dash in 9.9 s? c. By what percent did the sprinter need to increase his acceler- ation in order to decrease his time by 1%? a. At what height above the ground do the balls collide? Your an- swer will be an algebraic expression in terms of h, v0, and g. b. What is the maximum value of h for which a collision occurs before the first ball falls back to the ground? c. For what value of h does the collision occur at the instant when the first ball is at its highest point? 83. III A sprinter can accelerate with constant acceleration for 4.0 s before re aching top speed. He can run the 100 meter dash in 10.0 s. What is his speed as he crosses the finish line? 35. Ill The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 50 kmfs. To the crew's great sur- prise, a Klingon ship is 100 km directly ahead, traveling in the same direction at a mere 20 kmfs. Without evasive action, the Enterprise will overtake and collide with the Klingons in just slightly over 3.0 s. The Enterprise's computers react instantly to brake the ship. What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship? Assume the acceleration is constant. Hint: Draw a positionversustirne graph showing the motions of both the Enterprise and the Klingon ship. Let x0 = 0 km be the location of the Enterprise as it returns from warp drive. How do you show graphically the situation in which the collision is \"barely avoided"? Once you decide what it looks like graphically, express that situation mathematically