Transportation
Calculating the Horizontal Distance Traveled by a Marble in Free Fall
Calculating the Horizontal Distance Traveled by a Marble in Free Fall
In physics, the motion of a marble rolling off a desk and traveling horizontally can be analyzed using basic principles of motion. This article will guide you through calculating the horizontal distance the marble will travel from the surface of the desk. Let's dive right into the steps involved.
Understanding the Motion: Free Fall and Horizontal Displacement
When a marble is released from the top of a desk, it undergoes free fall under the influence of gravity. While in the air, it also has a horizontal velocity that propels it forward. The key equations to use here are the equations of motion under constant acceleration.
1. Calculating the Time of Free Fall
The first step in this calculation is to determine the time it takes for the marble to fall from the desk to the ground. This can be done using the equation for free fall:
h (1/2)gt2
Where:
h is the height of the desk (1.5 m) g is the acceleration due to gravity (9.81 m/s2) t is the time of free fall (s)Rearranging the equation to solve for t:
t √(2h/g)
Substituting in the values:
t √(2 * 1.5 / 9.81)
t √(3 / 9.81)
t ≈ 0.783 s
2. Calculating the Horizontal Distance
Once the time of free fall is determined, we can calculate the horizontal distance the marble travels. The horizontal motion of the marble is uniform because there is no horizontal acceleration. The horizontal distance x can be found using the equation:
x vx * t
Where:
x is the horizontal distance traveled (m) vx is the horizontal velocity (4 m/s) t is the time of free fall (0.783 s)Substituting in the values:
x 4 * 0.783
x ≈ 3.132 m
Key Steps and Formulas Recap
1. Calculate the time of free fall using t √(2h/g)
2. Calculate the horizontal distance using x vx * t
Conclusion
By applying the principles of motion under constant acceleration, we can accurately predict the horizontal distance traveled by a marble at a specific speed and height. This practical example illustrates how the laws of physics can be used to solve real-world problems. Understanding these calculations is essential for students studying mechanics and for professionals in various fields such as engineering, physics, and even sports science.