discussion question 1476

This week we’ve talked about polynomials and their properties. Polynomials show up in the real world a lot more than you would think! Applications can be found in physics, economics, meteorology, and more.

One real-world example of a degree-two polynomial is the projectile motion equation used in physics: h left parenthesis t right parenthesis equals minus 1 half a t squared plus v subscript 0 t plus h subscript 0

Details about this formula can be found at the brainfuse.com website.

For example, if you hit a baseball at shoulder height (say about 4 f t comma space 6 space i n c h e s space minus space h subscript 0 equals 4.5 f t), you may have an initial velocity of aroundv subscript 0 equals 89.5 m p h. The force of gravity is about a equals 32 f t divided by s squared..

We can convert our miles to hour to feet per second (89.5 mph = 131.3 ft/s) and create an equation that would model the height of the ball at time t:

h left parenthesis t right parenthesis equals minus 1 half left parenthesis 32 right parenthesis t squared plus 131.3 t plus 4.5

For the discussion this week we will use this equation in a baseball application. Techniques from 1.4 and 3.1 will be used. Show all of your work!

  1. Pick a baseball player’s average exit velocity from this list and convert it to feet per second.
  2. Estimate the height in feet that the ball would be hit and plug this and your velocity into the position equation. Give the equation.
  3. Find the maximum height of the ball (vertex).
  4. Find when the ball hits the ground (zeros).
  5. What role do you think the angel of the hit would play in modifying this equation or the values?

Compare the maximum height of your classmate’s baseball to your own. What factors do you think contribute most to the differences in your values? Explain.

 

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