Basketball player shoots a ball, find angle, parametrics

  • Thread starter Pi Face
  • Start date
  • #1
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Homework Statement



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?


Homework 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]


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.
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
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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.
 
  • #3
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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)
 
  • #4
rl.bhat
Homework Helper
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8
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)
Yes.
 
  • #5
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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 >.>
 
  • #6
rl.bhat
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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 >.>
Expression for t is correct.
Substitute in y(t) and solve for vo.
 
  • #7
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but what's theta? I have two unknowns, vo and theta.
 
  • #8
rl.bhat
Homework Helper
4,433
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but what's theta? I have two unknowns, vo and theta.
Vo = 25 ft/s.
 
  • #9
76
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can't believe i missed that. im all set now. thanks!
 

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