"You can kick a soccer ball a distance of $28$ $m$ when standing on level ground if the ball is launched at a ${40}^{\circ}$ angle. If you kick the ball in exactly the same way, but are at the foot of a ${15}^{\circ}$ upward slope, what is the horizontal distance traveled by the ball when it hits the ground?"

The answer is $19$ $m$

How do I go about solving this problem?

Using the equation $V_f^2 = V_i^2 + 2ad$, I found the initial velocity to be $23. 426$ $m/s^2$ but I'm not sure where to go from here...

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    $\begingroup$ You don't really need to know the speed of the ball. Just its path. $\endgroup$ – David K Sep 5 '15 at 22:49

The soccer ball does not know where on the ground it is going to hit. Find point of intersection where level trajectory cuts $ y= x \tan 15^0 $ sloping line.


The ball's path is a parabola, which can be expressed as $y = a x (28-x)$; $a$ is determined by the tangent angle. You need only to find the intersection of that parabola with a line.


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