Useful equations for projectile motion

1. where d_h is the horizontal displacement or range of the projectile, v_R is the resultant velocity, or the actual velocity of the projectile. Whatever the angle given is you need the sine, not of that angle, but the sine of twice that angle. Thus, if the angle given is 22⁰ you will need the sine of 44⁰. Also, keep ‘g’ positive since the displacement is along the horizontal.

2. d_v = or, since v_v is found by this equation: v_v = sinq v_R: d_v = . You can keep ‘g’ positive in this equation since 99.44% of problems will ask for the vertical displacement. Vertical displacement is positive.

3. t_¯ = . Where t_¯ is ½ the total time the projectile is in the air. Of course, since the same v_v is used in this equation as in the d_v equation, you could use this equation for t_½ : . Naturally these can be considered basic equations and should appear as such on your formula sheets. Obviously ‘g’ should be positive here because time cannot be negative.