# Physics Course/Projectile Motion

## Contents

## Projectile Motion[edit]

Projectile Motion refers to any motion moving under the effect of gravity. This kind of motion is famous for its trajectory being in the shape of a parabola.

## Analysis (two dimensional space)[edit]

Suppose the object is projected at an angle at a height h with an initial velocity of v with a gravity of g. When on Earth g will equal 9.8 m/s^{2}.

The components of velocity in horizontal (x-) and vertical (y-) directions are:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle x'(t)=v \cos \theta }****Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle y'(t)=v \sin\theta }**

By using , The x- and y- coordinates of the object are

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle y(t)=v (\sin \theta)t-\frac{1}{2}gt^2}**

which are functions in time.

By eliminating t,

which shows that the trajectory is a parabola

### Velocity at any time t[edit]

The magnitude of the velocity at any time t is given by

and the direction is given by

### Time of flight[edit]

To solve for the time of flight, we set y(t)=0

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): t=0**or**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle t=\frac{2v\sin\theta}{g}}**

### Horizontal range[edit]

After , the x-coordinate of the object is given by

### Maximum height[edit]

The maximum height is given by

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle H=\frac{v^2\sin^2\theta}{2g}+h}**

where h is the initial height