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Basketball player shoots a ball, find angle, parametrics

  1. Oct 10, 2009 #1
    1. The problem statement, all variables and given/known data

    A basketball player shoots a ball with a speed off 25 ft/sec from a point 15 ft horizontally away from the center of the basket. The basket is 10ft away above the the floor and the player releases the ball from a height of 8ft. At what angle should the player shoot the ball?


    2. Relevant equations
    Actually, this is one of my calc problems, but it seems physics-y enough to be posted here. I'm supposed to use parametrics to solve it.

    x(t)=x0+h0t
    y(t)= -(1/2)gt2+v0t+y0
    h0=s0cos[tex]\theta[/tex]
    v0=s0sin[tex]\theta[/tex]


    3. The attempt at a solution

    I don't feel like typing all these sub/superscripts, but I worked with the y(t) function, set v0 to 25 and y0 to 8 and got 0.0846 and 1.478 for values of t. But then I realizes that v0 was supposed to be s0cos[tex]\theta[/tex], which means I have both t and theta in the equation. How would I solve for either variable? Thanks.
     
  2. jcsd
  3. Oct 11, 2009 #2

    rl.bhat

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    x(t) = vo*coaθ*t, where vo is the velocity of projection.
    Find t = .......(1)
    y(t) = yo + vo*sinθ*t - 0.5*g*t^2.
    Substitute the appropriate values and find vo.
     
  4. Oct 11, 2009 #3
    Uh...
    how do I solve for t in x(t) = vo*cosθ*t?
    am I supposed to get a number? i get t= x/(vo*cosθ)
     
  5. Oct 11, 2009 #4

    rl.bhat

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    Yes.
     
  6. Oct 11, 2009 #5
    yes to a number or yes I solved it right?

    anyways, so then I substitute x/(vo*cosθ) for t in the y(t) equation? fun >.>
     
  7. Oct 11, 2009 #6

    rl.bhat

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    Expression for t is correct.
    Substitute in y(t) and solve for vo.
     
  8. Oct 11, 2009 #7
    but what's theta? I have two unknowns, vo and theta.
     
  9. Oct 11, 2009 #8

    rl.bhat

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    Vo = 25 ft/s.
     
  10. Oct 11, 2009 #9
    can't believe i missed that. im all set now. thanks!
     
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