Understanding the Speed of a Stone Thrown Upwards: A Comprehensive Guide

Have you ever wondered how to calculate the speed of a stone thrown upwards after a certain period of time? This article provides a detailed explanation using both kinematic equations and real-world scenarios. Whether the stone is caught and thrown back, or it falls due to gravity, we’ll break down the calculations step-by-step.

Using Kinematic Equations to Calculate the Speed

The problem at hand involves finding the speed of a stone thrown upwards after 5 seconds, assuming an initial velocity of 20 m/s and gravitational acceleration of 10 m/s2. To solve this, we use the following kinematic equation:

Equation: v u at

Where:

v final velocity (m/s) u initial velocity (m/s) a acceleration (m/s2) t time (s)

Calculations

In this scenario, the initial conditions are as follows:

u 20 m/s (initial velocity upwards) a -10 m/s2 (acceleration due to gravity, acting downwards) t 5 s (time)

Substituting these values into the equation:

v u at

v 20 m/s (-10 m/s2) times; 5 s

v 20 m/s - 50 m/s

v -30 m/s

The negative sign indicates that the stone is moving downwards after 5 seconds. Therefore, the speed of the stone after 5 seconds is 30 m/s downwards.

Note: The direction is important here, as it tells us the motion of the stone. The absolute value of the velocity is 30 m/s.

Scenarios and Implications

Should someone be standing in mid-air to catch the stone and throw it back, this scenario is highly improbable in a realistic setting. Therefore, we can assume that the stone will continue its motion under the influence of gravity alone.

Assuming the Stone is Thrown Near Vertically Off a Cliff

In this case, the stone would travel downwards due to gravity, with a speed of 10 m/s (as it is falling freely). The 30 m/s speed mentioned earlier is the actual speed of the stone, which is the absolute value of the vector velocity (-30 m/s).

Question for Clarification:

After 5 seconds, the velocity of the body will be 30 m/s in the downward direction. However, this is not possible if the body lands on the same level where it was thrown. This is because the time taken to reach the maximum height with an initial velocity of 20 m/s is 2 seconds. Therefore, the stone will return to your hand after 4 seconds, not 5.

Further Clarification:

The stone will either hit the ground (assuming it was thrown near a cliff) or return to your hand (if thrown from a flat surface). If it hits the ground, the time is 4 seconds, as the stone reaches its peak and falls back in a symmetrical trajectory.

Conclusion

Understanding the speed of a stone thrown upwards involves comprehending the kinematic equations and the influence of gravity. The scenario can vary based on the conditions, such as being thrown from a cliff versus a flat surface. Always remember that the speed is the absolute value of the velocity, and it is crucial to consider real-world constraints.

By applying these principles, you can solve similar problems and better understand the motion of objects under the influence of gravity.