Introduction

Motion in two dimensions is a fascinating topic that combines the principles of horizontal and vertical motion. This article delves into the analysis of a stone thrown horizontally from the top of a cliff, enhancing understanding and providing valuable insights for search engines and readers interested in physics and motion analysis.

Understanding the Problem

The scenario involves a stone being thrown horizontally from the top of a 44-meter cliff at a speed of 15 meters per second. Our goal is to determine the velocity of the stone after 2 seconds. Key components to consider include the horizontal and vertical motions of the stone. Let's break down the problem step-by-step.

Horizontal Motion

When the stone is thrown horizontally, only its vertical motion is influenced by gravity, assuming air resistance is negligible. The horizontal velocity remains constant throughout the motion. Therefore, the horizontal velocity after 2 seconds is still 15 m/s.

{{v}_{x}} 15, text{m/s}

Vertical Motion

The stone also experiences vertical motion due to gravity. Initially, the vertical velocity is 0 m/s (horizontal throw). We can calculate the vertical velocity after 2 seconds using the equation:

{{v}_{y}} {{v}_{y0}} g cdot t 0 9.81, text{m/s}^{2} cdot 2, text{s} 19.62, text{m/s}

Resultant Velocity

The resultant velocity after 2 seconds can be found using the Pythagorean theorem:

v sqrt{{v_{x}^{2} v_{y}^{2}}} sqrt{(15 , text{m/s})^{2} (19.62 , text{m/s})^{2}} approx 24.7 , text{m/s}

Direction of Velocity

The direction of the resultant velocity can be determined using the tangent inverse function:

u03B8 tan^{-1}left(frac{v_{y}}{v_{x}}right) tan^{-1}left(frac{19.62}{15}right) approx 53.13^circ

This means the velocity vector is approximately 53.13 degrees below the horizontal.

Conclusion

After 2 seconds, the stone has a velocity of about 24.7 m/s, with a direction of about 53.13 degrees below the horizontal. This problem demonstrates the application of kinematic equations and vector analysis in understanding the motion of projectiles.

Related Keywords and Keywords

The problem discussed above is a perfect example for the following keywords:

velocity calculation horizontal and vertical motion projectile motion