# How Do You Calculate Displacement at Reduced Velocity in Free-Fall Motion?

• The Eggman
In summary, a basic free-fall problem is a physics question that involves finding the position, velocity, or acceleration of an object falling under the influence of gravity with no external forces. To solve it, one must identify known and unknown variables and use equations of motion. The value of acceleration due to gravity is approximately 9.8 m/s^2 near Earth's surface, though it may vary. Air resistance can affect the problem but is usually assumed to be negligible. Common mistakes include not using correct units, equations, or considering direction of motion.
The Eggman

## Homework Statement

A stone is thrown straight upward with a velocity of 10V and travels upward a distance X. What is the displacement when the object is traveling at 5V?

## Homework Equations

xf=x0+v0t+1/2at^2

vf=v0+at

vf^2=v0^2+2ax

## The Attempt at a Solution

.75X? Further, what's the most efficient way of solving for it?

With half the speed the stone has 1/4 of the kinetic energy left so can only go 1/4*X higher or it is at 3/4*X when the speed is 5V.

## 1. What is a basic free-fall problem?

A basic free-fall problem is a physics question that involves finding the position, velocity, or acceleration of an object that is falling freely under the influence of gravity. It assumes that there are no external forces acting on the object besides gravity.

## 2. How do you solve a basic free-fall problem?

To solve a basic free-fall problem, you must first identify the known and unknown variables, such as the initial and final positions, velocities, and accelerations of the object. Then, you can use the equations of motion for free-falling objects, such as d = v0t + 1/2at2 and v = v0 + at, to solve for the unknown variable.

## 3. What is the value of acceleration due to gravity in a basic free-fall problem?

The value of acceleration due to gravity in a basic free-fall problem is approximately 9.8 m/s2 near the surface of the Earth. This value may vary slightly depending on factors such as altitude and location on Earth.

## 4. Can air resistance affect a basic free-fall problem?

Yes, air resistance can affect a basic free-fall problem if it is significant enough. In real-world situations, air resistance may slow down an object's acceleration or even cause it to reach a terminal velocity where the acceleration is zero. However, in a basic free-fall problem, it is typically assumed that air resistance is negligible.

## 5. What are some common mistakes when solving a basic free-fall problem?

Some common mistakes when solving a basic free-fall problem include forgetting to include units, using the wrong equation, and not considering the direction of motion. It is important to keep track of units and use the correct equations for the given scenario. Additionally, the direction of motion must be taken into account when determining the sign of variables such as velocity and acceleration.

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