We are given that,

We need to find
when 
The equation that relates x and
can be written as,


Differentiating each side with respect to t, we get,



Replacing the value of the velocity


The value of
could be found if we know the length of the beam. With this value the equation can be approximated to the relationship between the sides of the triangle that is being formed in order to obtain the numerical value. If this relation is known for the value of x = 6ft, the mathematical relation is obtained. I will add a numerical example (although the answer would end in the previous point) If the length of the beam was 10, then we would have to



Search light is rotating at a rate of 0.96rad/s
To determine the velocity of the roller coaster as it moves down, we use the kinematic equation which is expressed as 2gy = vf^2 - v0^2 where g is the gravitational acceleration, y is the elevation of the roller coaster, vf and vo are the final and initial velocity. We calculate as follows:
2gy = vf^2 - v0^2
Since it starts at rest, v0 is zero.
2gy = vf^2
vf = √2gy
vf = √2(9.8)(101)
vf = 44.5 m/s
Answer:
The work done on the athlete is approximately 2.09 J
Explanation:
From the definition of the work done by a variable force:

and substituting with the function of our problem:

Because,
In left image pin is not touch to the wire.
In right image pin is touch to the wire.
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