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Unformatted text preview: 1 January 26, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 10 Realistic Trajectories and Relative Motion Hitting a Home Run Hitting a Home Run Suppose a batter hits a baseball so that it has an initial launch angle of 35 and an initial speed of 110 mph (realistic) How far will the baseball go? We call the distance the ball travels the range R We have derived the range in terms of the launch angle and initial speed Not realistic! Air resistance has a big effect January 26, 2012 Physics for Scientists&Engineers 1 2 v = 110 mph = 49.2 m/s R = v 2 g sin2 = 49.2 m/s ( ) 2 9.81 m/s 2 sin 2 35 ( ) = 231.5 m R = 231.5 m = 759.5 ft Realistic Projectile Motion Realistic Projectile Motion We have been studying ideal projectile motion To calculate realistic trajectories we must take into account the effect of the air on the motion of the object Air resistance Spin Here is a comparison of ideal versus realistic for the flight of a baseball January 26, 2012 Physics for Scientists&Engineers 1 3 January 26, 2012 Physics for Scientists&Engineers 1 4 Relative Motion Relative Motion So far: we moved the origin of the coordinate system to a location that is convenient for calculations Example: shifting x so that x 0 = 0 at the start of a projectiles trajectory Until now we have always kept the coordinate system in the same place during the motion that we want to describe But there are some situations for which a moving coordinate system is necessary Example: Airplane landing on a moving aircraft carrier January 26, 2012 Physics for Scientists&Engineers 1 5 Example: Airport Walkway Example: Airport Walkway Person walking with a velocity v w , as measured by an observer moving along with him on the walkway. Walkway surface moves with v wt relative to terminal. Two velocities add as vectors Velocity of person as measured by someone standing in the terminal: v t = v w t + v w January 26, 2012 Physics for Scientists&Engineers 1 6 Moving Reference Frames Moving Reference Frames Demand that reference frame (= coordinate system) moves with constant velocity relative to a coordinate system that...
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