Intercepting a Tennis Ball: A Physics Challenge for Thomas

How many chances does Thomas have to intercept the tennis ball?

Final answer:

By determining when the ball reaches the required heights of 20ft and 95ft via physics and the quadratic formula, we can ascertain that Thomas has two chances to intercept the ball if he can match those timings and maneuver accurately on the zip-line.

Explanation:

Thomas is facing an exciting challenge of intercepting a tennis ball launched by a machine towards a wall. The ball is projected to a height in the air and a distance of 90 feet away from the wall. With his innovative approach, Thomas sets up a zip line attached to the wall, starting 20 feet above the machine, with the ending point positioned 95 feet from the ground.

The key to answering this question lies in understanding projectile motion physics. As the ball follows a parabolic trajectory, it will reach its maximum height midway in the flight before descending. Thomas must be at the right place and time when the ball is at 20 feet and 95 feet to intercept it successfully.

To calculate the timings when the ball reaches those required heights, the quadratic formula is employed along with relevant physics formulae. The trajectory and distance travelled by the ball behave like a quadratic function, allowing for the determination of two solutions by substituting the starting and ending points at 20ft and 95ft, respectively.

If Thomas can match those calculated times by moving accurately along the zip-line, he has two chances to intercept the ball. However, precision timing and skillful maneuvering are essential for him to achieve this task successfully.

Thomas' innovative method of using physics and the quadratic formula showcases the exciting intersection of science and real-world challenges. By applying scientific principles to a fun and engaging scenario, he demonstrates the practical relevance and excitement of physics in everyday situations.