How to Describe the Path of a Baseball in Calculus

In calculus, you can describe the path of a baseball as a parametrized curve by using a pair of functions that include "time" as a dimension. The pair of functions are called parametric equations; for example, x = x(t) and y = y(t), where "t" is time.

Instructions

    • 1

      Determine the height of the baseball from the ground when it was hit, typically in feet. Write this value down as "h." For example, h = 3 ft.

    • 2

      Get the angle at which the baseball was hit in degrees. If it was hit straight in a horizontal direction, the angle would be 0. Write down the value as "a." For example, a = 20 degrees.

    • 3

      Gather the initial velocity of the baseball when it was hit, typically in miles per hour. For example, 100 mi/hr. Convert the value from miles per hour to feet per second with a conversion of 1 mi/hr = 1.46667 ft/sec. For example, 100 mi/hr = 146.67 ft/sec.

    • 4

      Use the following two parametric equations to describe the path of the baseball:

      x = (v * cos a) * t

      y = h + (v * sin a) * t - 16 * t^2

      where "t" is time in seconds.

    • 5

      Substitute the numbers and simplify the equations. For example:

      x = (146.67 ft/sec * 0.40808) * t

      y = 3 ft + (146.67 ft/sec * 0.91295) * t - 16 * t^2

      where "t" is in seconds.

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