---
title: "Vertical Motion Under Gravity"
description: "Apply the constant-acceleration equations to an object thrown or dropped, taking the acceleration as g downwards and keeping one sign convention for the whole solution."
canonical: https://lightmysky.com/learn/mathematics/vertical-motion-under-gravity-mt_IgNj9bn14O
source: https://lightmysky.com/learn/mathematics/vertical-motion-under-gravity-mt_IgNj9bn14O.md
retrieved: 2026-09-12
---

> **Agent view.** This is the Markdown twin of the page, for tools and assistants.
> When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md
> API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md
> Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt
> Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json
> Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`.

# Vertical Motion Under Gravity

Apply the constant-acceleration equations to an object thrown or dropped, taking the acceleration as g downwards and keeping one sign convention for the whole solution.

Subject: Mathematics · Area: Mechanics · Ages 16 to 17
Page: https://lightmysky.com/learn/mathematics/vertical-motion-under-gravity-mt_IgNj9bn14O

## Ready when they can

- Find the greatest height of a ball thrown upwards, using velocity zero at the top
- Find the time for a dropped object to fall a given height
- Explain what a negative root means when an object lands below its starting point

## Lesson: Falling and throwing under gravity

Falling is constant acceleration wearing a familiar number: 9.8 metres per second squared downwards. Take upwards as positive and gravity enters as negative 9.8, which keeps every sign honest. At the top of a throw the velocity is exactly zero, so a ball thrown up at 14 metres per second satisfies 0 equals 196 minus 19.6 s, giving a greatest height of 10 metres.

A dropped object starts with u equals 0, so the distance fallen is half g t squared. Falling 19.6 metres takes 2 seconds, since 19.6 equals 4.9 t squared. Falling 44.1 metres takes 3 seconds, since 44.1 equals 4.9 times 9.

**Example.** When the landing sits below the start, the equation is quadratic and one root is negative. A ball thrown from a cliff lands when t is 4 or negative 1: the 4 seconds is the landing, and the negative 1 belongs to the parabola 1 second before the throw, so you reject it.

**Tip.** Keep one sign convention for the whole solution and never flip halfway. A ball thrown up at 15 metres per second climbs for about 1.5 seconds, reaches about 11.5 metres, and returns to the hand after about 3.1 seconds.

**Recap.** Gravity pulls at 9.8 down, the top means v is zero, and a negative root belongs before the clock.

## Practice

14 questions on this page, each with its working shown.

## Needs first

- [Modelling Motion in a Straight Line](https://lightmysky.com/learn/mathematics/modelling-motion-in-a-straight-line-mt_no78_6w1rS)
- [The Constant-Acceleration Equations](https://lightmysky.com/learn/mathematics/the-constant-acceleration-equations-mt_Nyc3BcikQ9)

## Opens up

- [Kinematics with Calculus](https://lightmysky.com/learn/mathematics/kinematics-with-calculus-mt_2kNspOOoDw)
- [Projectile Motion](https://lightmysky.com/learn/mathematics/projectile-motion-mt_O1C-QxCSJN)