Projectile Motion - Hitting an edge

[Mcoroklo]

Homework Statement

I've made a picture of the situation:

http://img11.imageshack.us/img11/7177/drawing1m.jpg


I need to find the expression for the start velocity v0. The ball should exactly hit the corner.

The function should have the distance L (Which both is x-distance and y-distance to the point) and the angle a as variables.

We can ignore air resistance.

Homework Equations

Normal projectile motion equations:
x=(v0*cos(a)*t
y=(v0*sin(a)*t-1/2*g*t^2)

vx=v0*cos(a)
vy=v0*sin(a)-gt

The Attempt at a Solution

I've been sitting with he assignment for 2 hours - trying both creative and stupid solutions!

First attempt was setting x=L and y=L and find the expression for v0.

I've also trying to set the v=0, but afterwards finding out the ball speed doesn't have to be zero.

Nothing has worked out so far.

Any suggestions?

Thanks a lot.

 

[pgardn]

Might try this approach...

How far below the corner would the projectile strike if you aimed directly at the corner?

 

[kuruman]

Hi Mcoroklo, welcome to PF>

Your two starting equations are correct. Use the first equation to eliminate time in the second. That should give you what you need.

 

[Mcoroklo]

... Thanks a lot!

I guess you guys know the feeling. A lot of time spend on outrageous thoughts, afterwards finding the solution is way simpler.
I actually had your solution to Kuruman, checked for input (40deg and 10m). It gave complex numbers and I tried another approach. Ofcourse it should give complex numbers for each angle outside the span of 45-90..

Thanks a lot to both of you.

Looking forward to participate in the forum, hopefully helping people to! :-)

 

[pgardn]

... Thanks a lot!

I guess you guys know the feeling. A lot of time spend on outrageous thoughts, afterwards finding the solution is way simpler.
I actually had your solution to Kuruman, checked for input (40deg and 10m). It gave complex numbers and I tried another approach. Ofcourse it should give complex numbers for each angle outside the span of 45-90..

Thanks a lot to both of you.

Looking forward to participate in the forum, hopefully helping people to! :-)

Actually I read the problem wrong initially, I thought you were trying to solve for the angle given an initial velocity. But, if it helped, I am happy. The other posters approach is easier, my proposal was a conceptual way that might help with other similar problems. And it may have helped eliminate unecessary stuff if you were guessing and checking with numbers.