Deriving A Motion Equation

  1. 1. The problem statement, all variables and given/known data
    Derive algebraic expressions for the range and total time-of-flight of a projectile launched with initial speed v, from a height h, and at an angle Q, above the horizontal. We were given the final equations but I am unsure of how to derive them.


    2. Relevant equations
    range=vt-.5gt^2, where g is the acceleration due to gravity and t is the time in seconds.

    time= (vsinQ+((vsinQ)^2+2gh)^.5)/g


    3. The attempt at a solution
    Considering the ball, after it has been launched:
    Fx=0
    Vox=vcosQ
    Fy=mg
    Voy=vsinQ

    ?
     
  2. jcsd
  3. That equation for range is wrong.

    The first step is to find an the height as a function of time.
    Set this to zero to find the time-of-flight.
     
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