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Basketball game problem- projectile motion

  1. Oct 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Basketball player throws the ball form the middle of the court one second before the game ends. How much must the initial speed of the ball be and at what angle it must be thrown, if it should hit the basket at the exact time of siren without preceding reflection from board? Length of playground is 26 m, the distance between the floor and the ring is 306 cm, and the ball is thrown from height 206 cm. Neglect the rotation of the ball. At what angle and with what velocity (speed) the ball hits the basket?

    2. Relevant equations

    Δx= v0xt
    Δy= v0yt – ½(gt²)
    v0= sqrt(v0x² + v0y²)
    tan α= v0y / v0x


    3. The attempt at a solution

    What I know:
    t= 1 s
    L= 26 m
    Δx= 13 m
    h1= 206 cm
    h2= 306 cm
    Δy= 100 cm = 1 m

    What I’m looking for:
    v0= ? m/s (initial velocity)
    α = ? ° (launch angle)
    vf= ? m/s (final velocity)
    β= ? ° (impact angle)

    ① First, I calculated the v0x = vx: v0x= Δx / t = 13 m/s
    ② Second, I calculated v0y: v0y= (2Δy + gt²) / 2t= 5.4 m/s
    ③ I know calculated v0 from the Pythagoras formula: v0= sqrt(v0x² + v0y²)= 14.08 m/s
    ④ And know I calculated the launching angle α: α= (tan)-¹(v0y / v0x)= 22.56°

    What is left know are final velocity and impact angle. Can I just state that final velocity = initial velocity (conservation of energy) and that impact angle = launch angle (symmetry of parabola)? Or, do I have to do new calculations because the basketball ring is higher than the launching height of the ball and the parabola is not symmetrical? If second is the case, I really need help, because I don’t know how to approach it now.

    Thank you for helping!
     
    Last edited: Oct 14, 2009
  2. jcsd
  3. Oct 14, 2009 #2
    You can't say that final velocity = initial velocity (conservation of energy), because
    you have to account for the increase in potential energy of the ball.

    another option is to use V_f = V_i + a t and compute a new v_x and v_y
     
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