Discover the Solution to a Challenging Basketball Physics Problem

[intriqet]

Homework Statement

A basketball player who is 2.0 m tall is standing on the floor L = 13.0 m from the basket. If he shoots the ball at a 43.0deg angle with the horizontal, at what initial speed must he throw so that the ball goes through the hoop without striking the backboard? The basketball height is 3.05 m.

Homework Equations

Kinematic equations.

The Attempt at a Solution

I don't even know where to start with this problem. I feel like I hadn't been given enough information. Please post hints to get me started. Thanks

 

[tiny-tim]

Hi intriqet!

Let the initial speed be v_i, and the time taken be t, and use the standard constant acceleration equations, once for the x direction (with a = 0), and once for the y direction (with a = -g).

Eliminate t, and that should give you a quadratic equation for v_i.

 

[intriqet]

 

[intriqet]

I'm not sure how to apply the constant acceleration kinematic formulas because I only have information for two of the variables for each direction.

For instance I have for the x (horizontal) direction:
Ax = 0
Vxi = xcos43

and for the y:
Ay = -9.81
Vyi = xsin43

If I had delta x or y this would be a ton easier but I can't compute delta x or delta y from the diagram.

 

[tiny-tim]

If I had delta x or y this would be a ton easier but I can't compute delta x or delta y from the diagram.

uhh?

from the diagram, ∆x = L = 13.0, and ∆y = 1.05.

 

[intriqet]

Sorry I wasnt sure If I could use delta y = 1.05 because that isn't the max height of the parabola and delta x = 13 because the full length of the parabola isn't 13.

Ok so based on that information I derived that

Ax = 0
Vxi = xcos43
Vxf = xcos43
deltax = 13
tx = ty

Ay = -9.81
Vyi = xsin43
Vyf = sqrt(-20.601 + (xsin43)^2)
deltaY = 1.05
ty = tx

Is this correct so far?

Oh and thanks by the way for your help and input

 

[tiny-tim]

Sorry I wasnt sure If I could use delta y = 1.05 because that isn't the max height of the parabola and delta x = 13 because the full length of the parabola isn't 13.

Forget parabola!

(and anyway, the height and width of a parabola are infinite)