A ball dropped from a height covers half of its journey from top of a tower in 0.5 seconds the height of the Tower is :(take g =9.8)? Explain

To find the height of the tower from which the ball is dropped, we can use the principles of physics, specifically the equations of motion under constant acceleration due to gravity. Given that the ball covers half of its journey in 0.5 seconds, we can break down the problem step by step.

Understanding the Motion of the Ball

When an object is dropped from a height, it accelerates downward due to gravity. In this case, we know the acceleration (g) is 9.8 m/s². The ball will cover different distances in different time intervals. The first half of the journey refers to the distance covered during the first 0.5 seconds.

Distance Covered in the First Half

To find the distance the ball falls in the first 0.5 seconds, we can use the equation of motion:

• d = ut + (1/2)gt²

Here, d is the distance covered, u is the initial velocity (which is 0 since the ball is dropped), g is the acceleration due to gravity, and t is the time in seconds.

Substituting the values into the equation:

• u = 0 m/s (the ball starts from rest)
• g = 9.8 m/s²
• t = 0.5 s

Now we can calculate the distance:

• d = 0 * 0.5 + (1/2) * 9.8 * (0.5)²
• d = 0 + (1/2) * 9.8 * 0.25
• d = 0.5 * 9.8 * 0.25 = 1.225 m

Finding the Total Height of the Tower

The distance we just calculated represents half of the total height of the tower since the ball covers half its journey in that time. Therefore, to find the total height (H) of the tower, we need to double this distance:

• H = 2 * d
• H = 2 * 1.225 m = 2.45 m

Final Height of the Tower

So, the height of the tower is 2.45 meters. This straightforward calculation illustrates not only the use of basic physics equations but also the relationship between time, distance, and acceleration due to gravity. In essence, we applied the equations of motion to solve for the height of the tower step by step, ensuring we understood each part of the process.