A ball launched on a imclined plane

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AI Thread Summary
In the discussion about a ball launched from a cart on an inclined plane, the primary question is whether the ball lands in the funnel, to the right, or to the left upon returning to the same height. The equations of motion provided are used to analyze the ball's and cart's trajectories, but the lack of numerical values adds to the confusion. The key point is that the ball is launched perpendicular to the inclined plane, not the ground. The user is trying to determine the relationship between the horizontal distances traveled by the ball and the cart, specifically comparing the effects of the launch speed and gravitational acceleration. Clarification on the launch direction and further numerical analysis are needed to resolve the problem accurately.
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Homework Statement


The cart is rolling down an inclined plane which is at an angle  to the horizontal.
When the cart’s speed is V, the ball is launched. When the ball returns to the same initial perpendicular distance above the track, does it land in the funnel, to the right of the funnel, or to the left of the funnel?


Homework Equations


yf = yi + Viy*t + 1/2ay*t^2
xf = xf + Vix*t + 1/2ax*t^2

The Attempt at a Solution


I was thinking then the Xball would be something like
Xf ball = Vix(ball)*t + V(launch x) * t
Xf car = Vix(car)*t + 1/2(gx)t^2
Vix ball / car are equal...so in this case i have to determine whether V(launch x) * t is larger or 1/2(gx)t^2 is larger...there were no numbers given so i and very confused right now thinking maybe my attempt is on the wrong track, can someone help me?
 
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Is the ball launched perpendicular to the ground(x axis) or to the cart(inclined plane)?
 
perpendicular to the cart
 
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