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Projectile Motion - find initial velocity, flight time and max height

  1. 1. The problem statement, all variables and given/known data
    a golf ball is shot from a height of 6.5 ft above the ground at an angle of 45° above the horizontal. The ball lands 39 ft and 3 inches downfield. Assuming ideal projectile motion find:
    a. Initial velocity
    b. flight time
    c. maximum height

    2. Relevant equations
    r = [(v0*cosθ)t ]i + ((v0*sinθ)t - 1/5gt^2)j.

    3. The attempt at a solution
    I have attached my work (problem 5) but can't seem to know if it correct. I have converted all of my units to metric because gravity is know as 9.8 m/s^2.
  2. jcsd
  3. kgal,
    From what I can gather, you don't have enough information given to you to solve for velocity, time of flight and maximum height directly. Try drawing what you see. The best method I use to solve projectile motion problems is to split the problem up into two parts - the object rising, & then falling.

    Also, I can't see your work.
  4. I used the definition of range to solve for initial velocity:
    a.R = (v0cosθ)*[(2v0sinθ)/g]
    solved for v0 = sqrt (Rg / 2cosθsinθ) = 10.82 m/s.

    b. I split the problem into two pieces, the time it takes the ball to reach the horizontal
    t1 = 2v0sinθ / g = 23.9 s
    Then got stuck on finding out the time it took the ball to drop the remaining 1.98 m...
    I tried finding t2 by using r = (v0cos45)t + (v0sin45t - 1/2 gt^2) and solve for t, but got to the point where t was a quadratic equation with 2 answers, t = 3.1 or 0.13 seconds...

    c. y max = y0 + (v0sinθ) ^2 / 2g = 4.96 m
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