Projectile Motion - Notes

A.        General Concepts:

  1. Motion on the x-axis and motion on the y-axis are independent of each other and must be considered separately.
  2. X-axis motion is uniform motion with a constant velocity (ax = 0)
  3. Y-axis motion is accelerated motion (ay =g)

 

B. VELOCITY (v)

  1. Remember any velocity can be broken down into perpendicular components (x and y), which are independent of each other, if the initial velocity (vi and the projection angle (q), are known.

                        a. Remember “q” is stated relative to the positive x-axis.

  1. The initial velocity (vi) of a projectile must be broken down into its initial x-velocity (vx) and its initial y-velocity (vy).

                        a. vxi = vi cosq : because a = 0 on the x-axis, vxi = vx

                        b. vyi = vi sinq

            1) When vy = 0 the projectile is at its highest point.

            2) When q = 0; vyi = 0, the objects begins at its highest point, and the object will fall downward.

 

C. TIME

  1. Remember the time the projectile is in the air is dependent on the y-axis motion only.
  2. Since y-axis motion is accelerated motion we use acceleration formulas to calculate times.
  3. Three times are important to consider when dealing with projectiles.

                        a) starting time – we deal with time elapsed therefore the starting time is always at 0s.

                        b) time to max altitude (tymax - when an object is projected in the air it will continue to rise until gravity                              decelerates vy to 0. Therefore, at maximum altitude vy = 0.

                                    1) tymax = vymax – vyi / g ; since vymax = 0, then tymax = - vyi / g

                                    2) Note tymax is half the hang time of the projectile.

                        c) Hang time (tT) - the total time the projectile is airborn

                                    1) t = vyf – vyi / g

                                    2) Note “tT” is double tymax

 

D. ALTITUDE (dy or y) - The height of the projectile above the reference point. (y-displacement)

  1. The altitude of a projectile is dependent upon 2 factors (vyi and g)
  2. Since y-axis motion is accelerated we use acceleration formulas to calculate altitude.

      y = vyit + ½ gt2

  1. Note to determine maximum altitude only use tymax

 

E. RANGE (dx or x) - the x-axis displacement of the projectile while it is in flight.

  1. The range of a projectile is dependent on 2 factors (vx and t)
  2. Since on the x-axis a = 0 use the uniform motion formula to calculate range x = vxt
  3. Note to determine range only use tT.