 Ch 1. Particle General Motion Multimedia Engineering Dynamics Position,Vel & Accel. Accel. varyw/ Time Accel. Constant Rect. Coordinates Norm/Tang. Coordinates Polar Coordinates RelativeMotion
 Chapter - Particle - 1. General Motion 2. Force & Accel. 3. Energy 4. Momentum - Rigid Body - 5. General Motion 6. Force & Accel. 7. Energy 8. Momentum 9. 3-D Motion 10. Vibrations Appendix Basic Math Units Basic Equations Sections Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll DYNAMICS - EXAMPLE Ball Throw Example A small ball is throw up a slope a distance of 30 ft. The slope is 30o from the horizontal and the ball's initial velocity is 40o from the vertical as shown. The ball leaves the persons hand 5 ft from the ground. What is the smallest initial velocity? Solution Vertical and Horizontal Distances The ball travels in both the x and y directions. Two equations will be needed. First, examine the y direction,      y = yo + voyt - 0.5gt2      30sin30 = 5 + vo cos40 t - 0.5(32.2) t2      10 = vo cos40 t - 0.5(32.2) t2 Next, use the x direction equation as second equation since there are two unknowns,      x = xo + vxot      25.98 = 0 + vo sin40 t      vo = 40.42/t Combining the two equations      10 = (40.42/t) cos40 t - 16.1 t2      20.96 = 16.1 t2      t = 1.387 s Substitute back into either equation to get initial velocity,      vo = 40.42 / 1.387 vo = 29.14 ft/s

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