Basketball Problem: Initial Speed to Make Shot

[tnhoots]

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??

 

[denverdoc]

first check your cos 30 value.

 

[tnhoots]

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?

 

[denverdoc]

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

 

[tnhoots]

I have 2 Vo becoming 10 in my equation. I have:
3.05=10-4.9t squared

 

[denverdoc]

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

 

[tnhoots]

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 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!

 

[denverdoc]

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.