Calculating Maximum Height: A Comprehensive Guide

When a stone is thrown vertically upwards with an initial velocity of 14.4 m/s, it reaches a certain maximum height. In this guide, we will walk through the steps to calculate the maximum height and the time it takes for the stone to reach this height and descent back to the ground. We will use the kinematic equations of motion to solve these problems, ensuring that our calculations are accurate and reliable.

Understanding the Kinematic Equations

One of the most important equations in the study of motion is the kinematic equation given by:

u v - at

Where:

u is the initial velocity (14.4 m/s in our case) v is the final velocity (0 m/s at the maximum height) a is the acceleration due to gravity (which is -9.81 m/s2, negative as it acts opposite to the direction of motion) t is the time taken to reach the maximum height

Calculating the Maximum Height

At the maximum height, the final velocity v becomes 0. Therefore, we can use the equation:

v^2 u^2 - 2as

Where:

s is the displacement (maximum height)

Plugging in the values:

0  14.42 - 2(-9.81)ss  (14.42) / (2 * 9.81)s ≈ 10.57 meters

After performing the calculation, we find that the maximum height reached by the stone is approximately 10.57 meters.

Calculating Time of Ascent

We can also use the first equation of motion to determine the time taken for the stone to reach the maximum height. The equation is:

v u - at

Where:

v is the final velocity (0 m/s) u is the initial velocity (14.4 m/s) a is the acceleration due to gravity (-9.81 m/s2) t is the time taken to reach the maximum height

Plugging in the values:

0  14.4 - 9.81tt  14.4 / 9.81t ≈ 1.47 seconds

The stone reaches the maximum height in approximately 1.47 seconds.

Calculating Time of Descent

The time taken for the stone to descend from the maximum height to the ground is the same as the time taken to ascend. This is due to the symmetry of the motion under constant acceleration.

Therefore, the time of descent is also approximately 1.47 seconds.

Conclusion

In conclusion, we have calculated the maximum height and the time taken to reach this height and descend back to the ground for a stone thrown vertically upwards with an initial velocity of 14.4 m/s. Understanding these calculations can help in various real-world applications, such as in sports or engineering, where the motion of objects under gravity plays a critical role.