Difference in Time the Balls Spend in the Air

Have you ever wondered about the fascinating concept of the difference in time two objects spend in the air when thrown vertically? Let's dive into the scenario of two students on a balcony, each throwing a ball vertically in opposite directions. How can we calculate the difference in time these balls spend in the air?

Calculating the Time for Each Ball

First, let's focus on the ball thrown vertically downward, b1. Given that it is thrown at an initial speed of 19.6 m/s from a height of 20.7 m above the ground, we can utilize the equations of motion to determine the time it takes for the ball to hit the ground.

The equation for vertical motion, s = ut + 0.5at^2, can be rearranged to solve for time (t). Plugging in the values of initial velocity (u), acceleration (a), and displacement (s), we find that the time taken for ball b1 to hit the ground is approximately 2.05 seconds.

Understanding the Result

Since the second ball, b2, is thrown vertically upward at the same initial speed, it will take the same amount of time to reach the highest point of its trajectory as ball b1 takes to hit the ground. Therefore, the difference in time the balls spend in the air is approximately 2.05 seconds.

By appreciating the principles of motion and applying mathematical formulas, we can unravel the mysteries of how objects behave in the air. Understanding such concepts not only enhances our knowledge of physics but also sparks curiosity and a sense of wonder about the world around us.