Answer:
Approximately ![\displaystyle\rm \left[ \begin{array}{c}\rm191\; m\\\rm-191\; m\end{array}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Crm%20%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bc%7D%5Crm191%5C%3B%20m%5C%5C%5Crm-191%5C%3B%20m%5Cend%7Barray%7D%5Cright%5D)
.
Explanation:
Consider this 
slope and the trajectory of the skier in a cartesian plane. Since the problem is asking for the displacement vector relative to the point of "lift off", let that particular point be the origin 
.
Assume that the skier is running in the positive x-direction. The line that represents the slope shall point downwards at to the x-axis. Since this slope is connected to the ramp, it should also go through the origin. Based on these conditions, this line should be represented as 
.
Convert the initial speed of this diver to SI units:
.
The question assumes that the skier is in a free-fall motion. In other words, the skier travels with a constant horizontal velocity and accelerates downwards at 
(
near the surface of the earth.) At 
seconds after the skier goes beyond the edge of the ramp, the position of the skier will be:
-coordinate: 
meters (constant velocity;)
-coordinate: 
meters (constant acceleration with an initial vertical velocity of zero.)
To eliminate from this expression, solve the equation between and for . That is: express as a function of .
.
Replace the in the equation of with this expression:
.
Plot the two functions:
- ,
,
and look for their intersection. Refer to the diagram attached.
Alternatively, equate the two expressions of (right-hand side of the equation, the part where is expressed as a function of .)
,
.
The value of can be found by evaluating either equation at this particular -value: 
.
.
The position vector of a point 
on a cartesian plane is ![\displaystyle \left[\begin{array}{l}x \\ y\end{array}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7Dx%20%5C%5C%20y%5Cend%7Barray%7D%5Cright%5D)
. The coordinates of this skier is approximately 
. The position vector of this skier will be ![\displaystyle\rm \left[ \begin{array}{c}\rm191\\\rm-191\end{array}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Crm%20%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bc%7D%5Crm191%5C%5C%5Crm-191%5Cend%7Barray%7D%5Cright%5D)
. Keep in mind that both numbers in this vectors are in meters.
