Basketball problem

  • Thread starter tnhoots
  • Start date
  • #1
36
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Homework Statement



A basketball player who is 2.00 m tall is standing on the floor L = 8.0 m from the basket, as in Figure P4.54. If he shoots the ball at a 30.0° angle with the horizontal, at what initial speed must he throw so that it goes through the hoop without striking the backboard? The basket height is 3.05 m.


Homework Equations



y=Yo+Voyt-(g/2)t squared
X=Xo+Voxt-(g/2)t squared


The Attempt at a Solution



Vxo=cos(30)
Vyo=sin(30)
Vo (cos 30)=8

3.05=2.00+Vo-4.9t squared
3.05=10-4.9t squared
t=square root (6.95/4.9)
=1.191

Vo=8/(.7071*1.191)
=9.499


However, this is wrong...any suggesions??
 

Answers and Replies

  • #2
960
0
first check your cos 30 value.
 
  • #3
36
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oops...the the cosign value of 30 is .8660254038. So I take that value and multiply it by the square root of 6.95/4.9. Which is 1.191. I divide 8 by that product. Correct? My answer comes out to be 7.7561749; however, that is appearantly wrong. What am I doing wrong?
 
  • #4
960
0
your sin value gets bollixed as well and the Vot (first order term) disappears--2Vo becomes 10. There may be more issues but start with those. Careful algebra for starts.
John
 
  • #5
36
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I have 2 Vo becoming 10 in my equation. I have:
3.05=10-4.9t squared
 
  • #6
960
0
think we'are cross threaded, maybe I'm missing something
but,

y=Yo+sin(30)Vo*t+1/2at^2 going to 3.05=10-4.9t squared has me confused
 
  • #7
36
0
bc 3.05 was the height of the basket. I set the equation :Yo+sin(30)Vo*t+1/2at^2 equal to the height of the basket. I am pretty confused. I'm not sure what I'm doing at this point:uhh: I have my final equation looking like Vo=8/(cosign30 * 1.191). I found the 1.191 by taking the square root of 6.95/4.9.......AHHH!!!
 
  • #8
960
0
Lets try a fresh start.

first assuming a conventional x/y horizontal and vertical coordinate system:

your eqn for Y is correct, x is not. Since there is no acceleration in in this direction, its simply
x=cos(30)Vo*t. But we do know how far the ball has to travel 8m.
so 8/cos(30)=Vo*t Now can we use that info in the Y eqn to make life simpler? For sure and I think you were close, so patience, my friend. Beware tho i think there may still be one wrinkle ahead.
 
Last edited:

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