Determining the Height from which a Ball is Dropped

When a ball is dropped from a certain height, it can often be quite challenging to determine the exact initial height from which it was dropped, especially if air resistance is ignored. This scenario involves a ball that falls from rest and, when it reaches the ground, its velocity is measured to be 14 meters per second (m/s). The task is to calculate the original height of the ball above the ground.

The basic equation that governs this situation is:

Using the SUVAT Equations for Motion under Gravity

The SUVAT equation we will use in this scenario is:

(v^2 u^2 2as)

Where:

v is the final velocity (14 m/s) u is the initial velocity (0 m/s as the ball is dropped from rest) a is the acceleration due to gravity (in this case, 9.8 m/s2) s is the height from which the ball was dropped

Substituting the known values, we have:

142 02 2 times; 9.8 times; s

This simplifies to:

196 19.6s

From here, we can solve for s:

s 196 / 19.6

s 10 meters

Therefore, the ball is dropped from a height of 10 meters. This method provides a precise calculation based on the principles of physics and the SUVAT equations.

Understanding the Variables and Implications

The acceleration due to gravity, denoted as g, is a constant value used in this calculation. In this case, the standard value of g is approximately 9.8 m/s2. However, it's worth noting that this value can vary slightly depending on the location on Earth. For instance, it can range from 9.764 m/s2 to 9.834 m/s2, with the exact value depending on the latitude and altitude of the location.

Using the standard value of 9.8 m/s2, the calculation is simplified, making it easier to solve for s, the height from which the ball was dropped. This approach leverages the SUVAT equations, specifically the one that relates the final velocity, initial velocity, acceleration, and displacement.

Conclusion

In conclusion, when a ball is dropped from rest and its final velocity upon hitting the ground is 14 m/s, the height from which it was dropped can be calculated using the SUVAT equations. The specific value of the acceleration due to gravity is a crucial piece of information, and using the standard value of 9.8 m/s2, we determined that the ball was dropped from a height of 10 meters.

This calculation is useful in a variety of practical applications, from physics problems to real-world scenarios such as ensuring proper safety measures in building design and construction.