Projectiles Launched at an Angle

Trigonometry helps you to deal with projectiles launched at an angle by resolving angled velocities into their x- and y-components so that you can analyze horizontal and vertical motion separately.  The time of flight is dependent primarily on the initial vertical velocity, and the longer the time of flight, the greater the horizontal range. If velocity is fixed, an angle of 45 degrees gives you the longest range.  This happens because 45 degrees is halfway between horizontal (0 degrees) and vertical (90 degrees). A horizontal velocity gives you a large horizontal distance while a vertical velocity gives you a large time of flight. 

In the next lesson, you will take a look at a different type of two-dimensional motion and discover how to analyze the motion of objects traveling in circular paths.