Final answer:
The question pertains to the mathematics of projectile motion, specifically calculating the time at which a ball thrown upward reaches a certain height using the quadratic equation derived from the function describing its height over time.
Step-by-step explanation:
The student's question involves the function h(t) = -10t² + 24t + 5.6, which describes the height of a ball thrown upward as a function of time. To determine important characteristics of the ball's trajectory, like the time it takes for the ball to reach a certain height or return to the ground, one may use the quadratic formula. The quadratic equation finds the roots of the function, which represent the times at which the ball reaches a certain height.
For a ball that returns to a position higher than its starting point, one would solve for t when h(t) is equal to the desired height. In this case, the student must find the zeros of the height function to understand when the ball will be at a certain height above its starting altitude. Typically, the larger positive root represents the time when the ball is on its way down, having already reached its maximum height.
In Physics, concepts like acceleration due to gravity, which is approximately 9.8 m/s² on Earth, are considered when analyzing projectile motion. However, in the given mathematical equation, the acceleration is represented by the coefficient of the t² term, which is -10 in this case, indicative of the acceleration in feet per second squared. The equation format and the coefficients may vary based on the unit system used (e.g., metric or imperial).