LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=CS 123Lab 3 Part 3 StarterLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=This problem is given as "Baseball power"by Aaron D. Klebanoff, Department of Mathematics,Rose-Hulman Institute of Technology, Terre Haute IN 47803 USA.Sandra K. Dawson, Mathematics, Glenbrook South High School, Glenview, IL 60025 USARosaline Secrest, Physics, Terre Haute South Vigo High School, Terre Haute, IN 47802 USA When a batter comes to the plate in baseball and swings at a pitch, the swing usually takes 0.2 seconds to reach the plate. During this time, the batter is transferring energy to the bat. The rate at which the energy is transferred to the bat increases from 0 to 9 horsepower during the first 0.15 seconds and then decreases to zero as the bat comes across the plate. (Note: one horsepower equals 746 joules/second.) The following data was collected for a particular swing:Time (in seconds)Power (in horsepower)00.00.0250.80.052.00.0753.0.13.0.1257.5.159.0.1753.0.23.0

(a) Create a piecewise linear expression, piecewise quadratic expression, a piecewise cubic expression, and a piecewise quartic (degree 4) expression that interpolates these data points. Plot them all together. Which one would you pick as doing a reasonable job of "reality"? At what point do you think the point of diminishing returns is reached as far as degree? The computer has to do more work for higher degree polynomials so you would want to use higher degree polynomials only to the extent to which they are helpful.As with the other problems, it is probably most convenient to do this calculation in an ordinary Maple document, not a code edit region since no scripts or procedures are involved.Enter your work for the expressions here.Enter your plot here.Enter your choice for which kind of spline you'd use.(b) Through definite integration, calculate the total amount of energy expended by the batter What are the units of energy being used? Convert the answer into an answer expressing the amount of energy in joules. Recall that you can use the built-in convert procedure to do unit conversions without looking up the details of how to do the conversion yourself -- look up the details in the on-line documentation if you don't remember how to do that.
Compare this to a typical everyday activity whose energy you can estimate to convince yourself that your answer has the right order of magnitude to be a plausible reason.. For example, if discover that your answer is comparable to the energy output of Grand Coulee Dam, you might want to spend more time checking your calculation.Enter your work for the energy calculation here.JSFH(c) Using your selection, estimate the maximum power reached, in watts.Enter your work for computing the maximum power reached. Also, compute the time when it happens. Explain how you checked the answer for at least plausibility.JSFH(d) Using your selection, estimate the time when the power is increasing the fastest. You will have to set this up as an optimization problem: what is the objective expression? What interval do you want to look for the extremum, and are you looking for a minimum or maximum?Enter your work here.JSFH(e) We are studying human-powered electrical devices. We want a gross estimate of whether the amount of power produced in a baseball swing is useful. We pose the following question: assuming conversion without loss of efficiency, how long could the power generated by the baseball swing power an iPad? An iPad typically draws 2.5 watts of power (25 watt hour battery; typical 10 hours of usage: http://www.apple.com/ipad/specs/). Be sure to label your answer with the appropriate units -- minutes, hours, seconds, days, or years?LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Enter your work here.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHJSFH