When he sees teachers encouraging other children to wait in the cafeteria until the first bell rings, Ian follows them. What typ
1 answer:
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Answer:
Approximately .
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
. The coordinates of this skier is approximately
. The position vector of this skier will be
. Keep in mind that both numbers in this vectors are in meters.
