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Kinematics Tennis Ball Problem

  1. Sep 8, 2015 #1
    1. The problem statement, all variables and given/known data
    ) You are given the task of shooting a tennis ball from ground level through 2 hoops. The two hoops’ centers and the launch site are located in the same vertical plane, and the hoops are oriented perpendicular to the ball’s proposed trajectory and also in a vertical plane.


    The first hoop has a height y1 and is located at a horizontal distance from the x1 launch site (which is located at x0, y0). The second hoop is located at x2, y2.


    a) Use the d-v-a-t formulas to eliminate time and solve for the y-position as function of the x-position. In particular, show that


    y = a x + b x2


    Identify the quantities a and b in terms of launch speed v0 and launch angle q0, and the gravitational field strength g (which will later take on the value of 10 m/s2).


    b) Solve for a and b in terms of x1, y1, x2, and y2.


    c) For the case of y1 = 4.0 m, x1 = 2.0 m and y2 = 3.0 m, x2 = 4.0 m, determine the values of v0 and q0.

    2. Relevant equations
    y = Vy*t + .5(g)(t)^2
    x = Vx*t
    Vx = Vocos(theta)
    Vy = Vosin(theta)

    3. The attempt at a solution
    I've solved the a) part of the question and gotten that the coefficient a = tan(theta) while the coefficient b = g/(2*(Vocos(theta))^2). I'm not sure how to put these two equations in terms of the position coordinates x1, x2, y2, and y1.
     
  2. jcsd
  3. Sep 8, 2015 #2

    RUber

    User Avatar
    Homework Helper

    Are you assuming the ball's trajectory will pass through the centers of the hoops? If so, then you have 3 points, (x0,y0), (x1,y1), and (x2,y2), to solve what appears to be a quadratic form.
    Also, since simple ballistic motion is symmetric, you should see that you want the max y value to occur at (x1+x2)/2, so, you should be able to back that out into some requirement for q0 and v0.
     
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