Speed of the Throw for More Than Two Balls in the Sky

What should be the speed of the throw so that more than two balls are in the sky at any time? (Given g=9.8m/s²)

Answer:

C. Any speed less than 19.6 m/s

To have more than two balls in the sky at any time, we need to consider the time it takes for a ball to reach its maximum height and come back down. During this time, there should be at least one more ball in the sky.

The first ball is thrown upwards. It takes some time for the first ball to reach its maximum height and start descending. At this point, the second ball is thrown upwards. The first ball continues to descend while the second ball reaches its maximum height and starts descending. At this point, the third ball is thrown upwards.

To ensure that more than two balls are in the sky at any time, the time taken for a ball to reach its maximum height and come back down should be less than the interval between successive ball throws (2 seconds in this case). This way, when one ball is coming down, there should already be another ball in the sky.

The time taken for a ball to reach its maximum height and come back down can be calculated using the equation:

t = 2 * (v/g)

where t is the time, v is the initial vertical velocity, and g is the acceleration due to gravity.

For the balls to be in the sky simultaneously, we need:

2 * (v/g) < 2

Simplifying the inequality, we get:

v < g

Given that g = 9.8 m/s², the speed of the throw should be less than 9.8 m/s to ensure that more than two balls are in the sky at any time. Therefore, the answer is C. Any speed less than 19.6 m/s.