A person is throwing balls into the air one after the other. He throws the second ball when first ball is at the highest point. If he throwing 2 balls every second, how high do they rise?

To understand how high the balls rise when thrown into the air, we need to consider a few key concepts from physics, particularly the motion of projectiles and the effects of gravity. The scenario you described involves a person throwing balls in a sequence, with the second ball being thrown when the first ball reaches its peak height. Let's break this down step by step.

The Basics of Projectile Motion

When an object is thrown upwards, it experiences a force due to gravity that acts downwards. This force causes the object to decelerate until it reaches its highest point, known as the apex. At this point, the velocity of the ball is zero before it starts to fall back down.

Key Variables

To determine how high the balls rise, we need to know the initial velocity (v₀) with which the balls are thrown. The height (h) that the ball reaches can be calculated using the following kinematic equation:

• h = (v₀²) / (2g)

In this equation:

• h is the maximum height reached by the ball.
• v₀ is the initial velocity of the ball.
• g is the acceleration due to gravity, approximately 9.81 m/s² on Earth.

Timing of the Throws

Since the person throws the second ball when the first ball is at its highest point, we can analyze the timing. If he throws two balls every second, this means that the first ball is thrown at time t = 0 seconds, and the second ball is thrown at t = 1 second. The first ball will take some time to reach its peak height, which can be calculated using the formula:

• t_peak = v₀ / g

Here, t_peak is the time taken to reach the highest point. After reaching the peak, the ball will start descending, while the second ball is thrown at t = 1 second.

Example Calculation

Let’s say the initial velocity (v₀) of the balls is 20 m/s. We can calculate the maximum height:

• h = (20 m/s)² / (2 * 9.81 m/s²) = 400 / 19.62 ≈ 20.39 meters

This means each ball rises to approximately 20.39 meters before starting to fall back down.

Conclusion on the Sequence of Throws

In this scenario, the first ball reaches its peak height of about 20.39 meters before the second ball is thrown. The second ball will also rise to the same height, assuming it is thrown with the same initial velocity. Therefore, both balls reach the same maximum height, demonstrating the principles of projectile motion and the effects of gravity on their trajectories.

In summary, the height to which the balls rise depends on their initial velocity and the acceleration due to gravity. By understanding these principles, we can predict the behavior of objects in motion effectively.