Calculus and Coasters

by Kailyn Jeffers

Submitted : Spring 2021

The maximum height of a roller coaster was calculated using the given specifications by creating a position vector using the angle and initial velocities of the x and y directions and taking the derivative of that function to obtain the velocity as a function of time. After solving the y-direction of the velocity function for t, the time that it took for the train to make it to its maximum height was obtained. Plugging the t-value back into the position function resulted in the maximum possible height of a launch coaster with the given specifications. Following this, the t-value was plugged into the velocity function and its derivative to get the velocity and acceleration respectively of the function at the maximum height.     

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