The Vertical Motion Calculator helps you calculate the motion of an object moving vertically. It is useful in many fields such as physics, engineering, and sports, where understanding vertical motion is important. The calculator can determine the final velocity, height, and time of an object’s vertical motion.

## Formula of Vertical Motion Calculator

The formula for vertical motion can be divided into two main parts: the motion upwards and the motion downwards.

#### Motion Upwards

- Final velocity (vf) is calculate as: vf = vi – g * t
- Height (h) is calculate as: h = vi * t – (1/2) * g * t^2

#### Motion Downwards

- Final velocity (vf) is calculate as: vf = vi + g * t
- Height (h) is calculate as: h = vi * t + (1/2) * g * t^2

#### Definitions

- vf: final velocity (m/s)
- vi: initial velocity (m/s)
- g: acceleration due to gravity (approximately 9.8 m/s^2)
- t: time (s)
- h: height or displacement (m)

## Pre-calculated Values Table

To make calculations quicker, here is a table with pre-calculated values for common scenarios. This table can be use to find results without calculating each time.

Initial Velocity (m/s) | Time (s) | Final Velocity Upwards (m/s) | Height Upwards (m) | Final Velocity Downwards (m/s) | Height Downwards (m) |
---|---|---|---|---|---|

10 | 1 | 0 | 4.9 | 19.8 | 14.7 |

15 | 2 | -4.6 | 9.8 | 34.6 | 39.2 |

20 | 3 | -9.4 | 14.7 | 49.4 | 73.5 |

## Example of Vertical Motion Calculator

Let’s go through an example using the Vertical Motion Calculator.

Suppose you throw a ball upwards with an initial velocity of 20 m/s and want to find the height and final velocity after 2 seconds.

- Calculate the final velocity upwards: vf = vi – g * t vf = 20 – 9.8 * 2 vf = 20 – 19.6 vf = 0.4 m/s
- Calculate the height upwards: h = vi * t – (1/2) * g * t^2 h = 20 * 2 – (1/2) * 9.8 * 2^2 h = 40 – 19.6 h = 20.4 m

So, after 2 seconds, the ball’s final velocity upwards is 0.4 m/s, and it reaches a height of 20.4 meters.

## Most Common FAQs

**What is vertical motion?**

Vertical motion refers to the movement of an object in a straight line up or down under the influence of gravity.

**How does gravity affect vertical motion?**

Gravity causes objects to accelerate downwards at a constant rate of approximately 9.8 m/s^2. This acceleration affects the object’s velocity and height during vertical motion.