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Falling Object Model

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Falling Object Model

Study Guide

Key Definition

An object is a freely falling body if only gravity affects its motion with initial velocity and height: $h(t) = -16t^2 + v_0 t + h_0$

Important Notes

The term $-16t^2$ represents half of the gravitational acceleration (−32 ft/s²) multiplied by t², giving the displacement due to gravity.
Initial velocity $v_0$ is crucial for determining motion
When $h_0$ is zero, the object starts from the ground
The velocity at time $t$ is $v(t) = -32t + v_0$
In metric units, use $h(t) = -4.9t^2 + v_0 t + h_0$

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

The model uses physics principles of gravity, represented mathematically by $-16t^2$ for feet and $-4.9t^2$ for meters.

Remember

Memorize $h(t) = -16t^2 + v_0 t + h_0$ for calculations.

Quick Reference

Height Formula:$h(t) = -16t^2 + v_0 t + h_0$

Velocity Formula:$v(t) = -32t + v_0$

Understanding Falling Object Model

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $h(t) = -16t^2 + v_0 t + h_0$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If a ball is thrown upwards from the ground ($h_0 = 0$) with $v_0 = 80$ ft/sec, what is its height after 3 seconds?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A bottle is dropped from a height of $120$ feet. How long does it take to hit the ground?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Calculate the velocity of an object after $5$ seconds if it was thrown downwards with $v_0 = 20$ ft/sec.

Challenge Quiz

Single Choice Quiz

Advanced

A rocket is launched upwards with $v_0 = 150$ m/s. What will be its velocity after $8$ seconds?

Recap

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Review key concepts and takeaways