Within physics, the concept of "projectile motion" refers to launched objects' tendencies to fall both outward and downward, in parabolic arcs. In other words, these objects have both horizontal and vertical speeds, or "velocities." To avoid getting confused, picture horizontal and vertical velocities as arrows (or "vectors") pointing in different directions--and with a certain angle between them. Using simple trigonometry, you can calculate a launched object's vertical speed as a function of its horizontal speed.
Calculate the initial vertical velocity using trigonometry. For example's sake, consider an object with a total launch speed of 25 meters per second at an angle of 35 degrees. You can determine its vertical velocity, "uy," with the equation uy=usinθ, where "u" is the total launch speed, "sin" is your calculator's "sine" function and "θ" is the launch angle. For the example, the calculation is as follows: uy = (25) x (sin 35) = 25 x -.428 = -10.7 meters per second.
Use the initial vertical velocity to determine the object's vertical velocity at any given time. Keeping in mind the equation vy = uy - gt, where "uy" is the initial vertical velocity, "g" is the acceleration of gravity (-9.8 meters per second squared) and time is the amount of time that has passed. For the example launch, you would calculate the object's velocity at one second in the following manner: vy = (-10.7) - (-9.8)(1) = -.9m/s.
Determine the time at which the object stops falling using its initial vertical velocity. Keeping in mind that an object's velocity will equal zero once it hits the ground, set "vy" equal to zero and solve the equation for "t," or 0 = (-10.7) - (-9.8 x t). Add "10.7" to both sides to find that 10.7 = -(-9.8 x t), or 10.7 = 9.8t. Divide both sides by "9.8" to determine that the object falls for 1.09 seconds.
Don't be surprised if you get a negative value for initial vertical velocity--in fact, if you don't, you should be worried! As falling objects move downward, their vertical velocity values must be negative. This also explains why the accelerate of gravity is always negative.
Tips and warnings
- Don't be surprised if you get a negative value for initial vertical velocity--in fact, if you don't, you should be worried! As falling objects move downward, their vertical velocity values must be negative. This also explains why the accelerate of gravity is always negative.