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Projectile Motion - confirmation on answer(s) needed

  1. Feb 17, 2013 #1
    1. The problem statement, all variables and given/known data
    "A marble rolls off a table with a horizontal velocity of 1.93m/s and onto the floor. The table is 76.5cm above the ground. Air resistance is negligible.
    Find the horizontal distance, the air time and the final velocity."


    2. Relevant equations
    Δdy=ViyΔt + 0.5ayΔt2
    Rearranged: √(2Δdy/ay) = Δt *Equation A*

    VconstxΔt=Δdx *Equation B*

    Vfy2 = √(2ayΔdy) *Equation C*


    3. The attempt at a solution
    Use equation A to find Δt, substituting in the variables gives 0.395 seconds. Therefore the ball was in the air 0.395 seconds.

    Use equation B to find horizontal distance, substituting in the variables gives 0.762m [F]

    Use equation C to find the final vertical velocity, which ends up being 3.87m/s [D]

    Now since I know the final vertical velocity (3.87m/s downward) and the final horizontal velocity (1.93m/s [F], it remains constant since there is no air resistance) I can find the final velocity and its angle using pythagorean and trig.

    The final velocity is 4.32m/s [63° above the ground] after those calculations. Is that correct? My textbook has 4.3m/s [64° below horizontal] which is oddly worded and doesn't seem to be the same.
     
  2. jcsd
  3. Feb 17, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    The textbook just rounded to 1 decimal place, the value looks the same. The velocity is downwards, "below horizontal".
     
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