A juggler is maintaining 10 balls in motion, each rising to a height of 80 m from his hands. The question asks for the time interval that the juggler must maintain between each ball to keep them at the proper distance.


To understand the problem, we need to consider the motion of the balls and the time it takes for each ball to reach its maximum height. Let's assume the time it takes for each ball to rise to 80 m is "t" seconds.


When a ball is thrown upwards, it follows a parabolic trajectory. The time it takes for the ball to reach its maximum height is equal to the time it takes for the ball to fall back to the same height.


To calculate the time "t," we can use the formula for the maximum height reached by an object thrown upwards:
h = (1/2) * g * t^2,
where "h" is the maximum height, "g" is the acceleration due to gravity (approximately 9.8 m/s^2), and "t" is the time.

Rearranging the formula, we get:
t^2 = (2h) / g,
t = sqrt((2h) / g).

Substituting the given values, the time taken for each ball to reach 80 m is:
t = sqrt((2 * 80) / 9.8) seconds.


To maintain proper distance between the balls, the juggler needs to wait for each ball to reach the same height before throwing the next ball. Therefore, the time interval between each ball is equal to the time it takes for a single ball to reach 80 m.

The time interval is:
t = sqrt((2 * 80) / 9.8) seconds.


The juggler must maintain a time interval equal to the time it takes for a single ball to reach a height of 80 m. This time interval can be calculated using the formula t = sqrt((2 * 80) / 9.8) seconds.