Question

In January 2022, Aroldis Chapman (an MLB pitcher) set the record for the fastest pitch at a speed of 105.1 miles per hour (or 155.17 feet per second). If we imagine he threw the baseball almost vertically off the edge of a cliff 83 feet above sea level, we could model the height of the ball (h) given the time in seconds after he threw the ball (t) using the following quadratic equation: h= −16.087t2+155.16t+83

Answer 1

The quadratic equation modeling the vertical motion of a baseball thrown by Aroldis Chapman includes terms for initial velocity, acceleration due to gravity, and initial height, allowing for predictions of the ball's trajectory.

Step-by-step explanation:

Modeling Vertical Motion of a Baseball

Aroldis Chapman, known for his fastball pitches, is said to have thrown a baseball with a record speed. Using the provided quadratic equation, h = −16.087t² + 155.16t + 83, we can model the vertical motion of a baseball after being thrown almost vertically from a cliff 83 feet above sea level. This equation takes into account the initial velocity of the ball and the acceleration due to gravity, which is represented by the coefficient of the t² term.

This model assumes that there is no air resistance and the motion is purely under the influence of gravity. It allows us to predict how high the ball will go and how long it will stay in the air before hitting the sea level, based on Chapman's record-setting pitch velocity.