Um... have you tried anything?
A ball is thrown with initial speed up an inclined plane. the plane is at an angle and the ball's initial velocity is at angle . Choose an axis with x measured up the slope, y normal, and z across it. Write down Newton's second law using these axes and find the ball's position as a function of time. Show that the ball lands a distance
from it's launch point.
Show that for a given and that the max range is
I've tried many things but none of them get me even close to getting that result. I know that the force in the x direction is and so the displacement formula has this subed for g without the for the displacement in the x direction. The displacement in the x direction is and the y is normal so there's no displacement in the y.
Ok I'm coming back to this now.
I took a look at the derivation for this problem in two dimensions for a projectile and tried to model my approach after it. This is how far I got.
then from this we can get
Then as in the 2d simple case I multiplied to obtain
but this doesn't give the result I was looking for.
Can anyone help me with this?
I think there is a 'g' missing in your first part.
Make a sketch.
(I'll be using v instead of vo to make it easier to type)
The velocity of the ball up the plane is
That perpendicular to the plane is
The acceleration is down the plane and is given by
And that perpendicular to the plane is given by
From this, the distance perpendicular to the plane where the particle lands is 0 and is given by:
This:
For the distance along the plane, we have:
Can you complete the first part now?
EDIT: Didn't see you replied Skeeter
For the second part now. (there is also a mistake, see below)
Use the identity:
This gives:
Simplify:
At the maximum range, since only theta can vary.
Hence we get:
Something cancels out, giving:
From this, you can even find the relation between theta and phi for this value of range