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 Fluids Math Mechanics Statics Thermodynamics Author(s): Kurt Gramoll ©Kurt Gramoll

 DYNAMICS - EXAMPLE Toy Rocket Example A small toy rocket follows a vertical path that can be modeled by y(t) = 5t3/6 - t4/12 (ft). What will be the maximum height? Also, what is the height when the acceleration is zero? Solution Position when v = 0 and a = 0 First, find the equation that models both the velocity and acceleration as function of time.      v(t) = dx/dt = 5t2/2 - t3/3      a(t) = dv/dt = 5t - t2 a) The maximum height will occur when velocity is zero (it has reached it zenith).      v = 0 = 5t2/2 - t3/3      t = 7.5 s Substitute time back into the position equation gives,      yt=7.5 = 5 (7.5)3/6 - (7.5)4/12               = 87.89 ft b) Use the acceleration equation to find the time when the acceleration will be zero.      a = 0 = 5t - t2       t = 5 s (zero is not a realistic solution) Substitute time back into the position equation gives,      yt=5.0 = 5 (5)3/6 - (5)4/12               = 52.08 ft So, the rocket has a negative acceleration after the rocket goes up only 52.08 ft, but it keeps climbing until it reaches its zenith of 87.89 feet.

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