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hw1 - Human Motion Kinetics ME 577/BME 595D Homework...

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Unformatted text preview: Human Motion Kinetics ME 577/BME 595D Homework 1 Due Midnight Monday 24 January 1. The first appearance of Superman was in Action Comics #1 in 1938. Created by writer Jerry Siegel and artist Joe Shuster, his powers granted him the ability to “leap tall buildings in a single bound,” made him “faster than a speeding bullet,” and he was “more powerful than a locomotive.” Let’s say that this early version of Superman cannot fly and wants to leap to the top of a tall building (400 ft.) in a single bound. If we model him as a particle and he takes off at an angle of 80o, what is the minimum initial speed required to get him to the top of the building? How far away from the base of the building should he take off? You may neglect drag on this problem. 2. What if Superman has to get to the top of a 300 ft. tall building. Plot his initial speed vs. the takeoff angle (60 ­85o). Which variable affects the initial speed more? The height of the building or the takeoff angle. You may neglect drag on this problem. 3. The Flash (mass approximately 80 kg. and frontal cross sectional area 0.7 m2) pushes on the road and the road pushes back on him, providing the propulsion force that moves him forward. What is the lateral force exerted on the flash if he moves at a constant speed of 340 m/s. Plot the lateral force required to move him at a constant speed between 10 m/s and 340 m/s. Please include drag in this problem. 4. If the maximum friction coefficient is 1, how fast can the Flash run before his feet just slip on the road’s surface? Please include drag in this problem. 5. What is the maximum force the road exerts on the Flash if he has to accelerate to 340 m/s? Assume he reaches his top speed in half a second, but does it with constant acceleration. Try this problem with and without drag. 6. Find the world record for the male and female high jump. If the high jumper is modeled as a particle, determine the take off velocity required to just clear the bar in each case. N.B. you should be careful estimating the initial or takeoff position of the particle. You may neglect drag for this problem. 7. A broadjumper approaches his takeoff board A with a horizontal velocity of 30 ft/sec. Determine the vertical component of the velocity of his center of mass at takeoff for him to make the jump shown. What is the vertical rise, h, of his center of mass? You may neglect drag in this problem. 8. An outfielder experiments with two different trajectories for throwing to home plate from the position shown: (a) v0 = 140 ft/s with θ = 8o and (b) v0 = 120 ft/s with θ = 12o. For each set of initial conditions, determine the time required for the baseball to reach home plate and the altitude, h, as the ball crosses the plate. You may neglect drag for this problem. 9. A player pitches a baseball horizontally toward a speed ­sensing radar gun. The baseball weighs 5 ­1/8 ounces and has a circumference of 9 ­1/8 inches. If the speed at x = 0 is v0 = 90 mph, estimate the speed as a function of x. Assume that aerodynamic drag is given according to the equation we developed in class (the wind speed can be assumed to be negligible). Use a value of 0.3 for the drag coefficient. You may neglect the vertical component of the motion. Evaluate your answer for a distance of 60 ft (the approximate distance between the pitcher’s hand and home plate). Please include drag in this problem. Please email it to me in pdf form at: [email protected] ...
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