Final answer:
The ball will take approximately 4.28 seconds to fall 90 meters to the ground, calculated using the free-fall formula under gravitational acceleration.
Step-by-step explanation:
The student's question is about calculating the time taken for a ball thrown horizontally from the top of a building to reach the ground. The building height is given, so we can determine the fall time using the formula for the time of free-fall, which is derived from the equations of motion under constant acceleration due to gravity. The horizontal velocity does not affect the time taken to fall, so it can be ignored for this calculation.
Step by Step Solution:
Use the equation ¿ y = ½gt² to find the time (t) for the ball to fall 90 meters (¿ y), where g is the acceleration due to gravity (9.81 m/s²).
Rearrange the equation to solve for t: t = √(2y/g).
Plug in the values: t = √(2 * 90 m / 9.81 m/s²).
Calculate the result: t ≈ 4.28 seconds.
The ball will take approximately 4.28 seconds to reach the ground.