Projectile Motion

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1. A projectile is any object that is launched into the air

2. We will only consider launch angles less than 90˚ (i.e. not vertically) and in calculations, we will ignore air resistance

3. The only forces acting on a projectile are gravity and air resistance

4. If there is no air resistance, the trajectory (path) is parabolic

5. The projecting velocity ($v$) has a vertical component $v_V$ and a horizontal component $v_H$. These may also be written as $v_y$ and $v_x$, respectively

6. The vertical and horizontal components of the motion are independent of one another. Each can be calculated using appropriate equations of motion

7. A projectile’s motion is simply the resultant of its horizontal and vertical motions

8. Horizontally (ignoring air resistance)

   1. There is no force, so the horizontal velocity is constant
   2. Time of travel and range (horizontal displacement) are found using $s_H=v_{H}t$

9. Vertically (ignoring air resistance)

   1. The only acting force is gravity
   2. The acceleration is $9.8m{s}^{-2}$ downwards throughout the motion
   3. The final displacement is zero (if landing at the same height)
   4. The time of travel from launch to landing is found using $s_V=v_V+\frac{1}{2}g{t}^2$
   5. At maximum altitude, $v_V=0$, so ${v_V}^2={u_V}^2+2a{s}_V$ can be used to find the maximum altitude reached

10. IMPORTANT!

    1. You cannot mix horizontal and vertical components in the same calculation