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Projectile Motion

  1. Jul 21, 2009 #1
    1. The problem statement, all variables and given/known data
    the center field fence in a ball park is 10ft high and 400 feet from home plate. the ball is hit 3 ft above ground. it leaves the bat at an angle of theta degrees with the horizontal speed of 147.67ft/second. find the minimum angle at which the ball must leave the bat in order for hit to be a home run.
    the path of the projectile is modeled by the parametric equations:
    x=v0cos(theta)t
    y=3+(v0sin(theta)t-15t^2

    2. Relevant equations



    3. The attempt at a solution
    substitute 400 in for x and 147.67 for v0to solve for t
    t=400/(146.67cos(theta)
    then i took t and put it into the equation for y
    y=3+(147.67sin(theta)(400/(146.67cos(theta))-16(400/(146.67cos(theta))^2


    Did I do this correctly? If so, can some one help me with the math to solve for theta?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 21, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper


    You can rewrite the equation as
    y = 3 + 400*tanθ - 16*400^2*sec^2θ/146.67^2 [ 1/cosθ = secθ]
    Put sec^2θ = 1 + tan^2θ,and solve the quadratic for tanθ.
     
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