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Question: chapter 2 hw scaling equations 1 for the case of...

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Chapter 2 HW Scaling Equations 1 For the case of the thrown ball, we had other choices to scale the dependent variable of position, yp, and the independent variable of time, t. We can let the scale for position remain as h, so that Y, -y /h, but how about choosing a different time scale? From the parameters h, g, and vo it is not too difficult to arrive at three combinations that have the units of time 1/2 Lets try the third option for a time scale, so that the new dimensionless time ist-Yo t / h . We can restrict ourselves to vo >0 so there are no singularities in the time definition. If it is easier, use your software (Maple, MatLab, etc) to perform the variable transformation, solve the dimensionless ODE, and plot the results similar to the example in the text. a. Make the governing equation, dy, dt g, dimensionless using the definitions of T and Yp b. Make the initial conditions, yp(t-O)-h, dyp /dt.-vo , dimensionless too. c. Where does Fr appear now in the problem? Is that different from before? d. Solve the system for Y, (T) using your software (or pencil). e. Solve for the impact time, T(Fr) , and plot it or 0.1sFrs1. Describe your results.

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