Arc Length In Exercises 49-54, find the arc length of the curve on the given interval. Parametric Equations Interval x = 3 t + 5 , y = 7 − 2 t − 1 ≤ t ≤ 3
Arc Length In Exercises 49-54, find the arc length of the curve on the given interval. Parametric Equations Interval x = 3 t + 5 , y = 7 − 2 t − 1 ≤ t ≤ 3
Solution Summary: The author explains how to calculate the arc length of a curve using the parametric equations.
A wheel with radius 2 cm is being pushed up a ramp at a rate of 7 cm per second. The ramp is 790 cm long,
and 250 cm tall at the end. A point P is marked on the circle as shown (picture is not to scale).
P
790 cm
250 cm
Write parametric equations for the position of the point P as a function of t, time in seconds after the ball
starts rolling up the ramp. Both x and y are measured in centimeters.
I =
y =
You will have a radical expression for part of the horizontal component. It's best to use the exact radical
expression even though the answer that WAMAP shows will have a decimal approximation.
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter
x-2, y-t
++
-1
0.5
05
05-
-05-
0.5
+
--05
Use a graphing utility to graph each set of parametric equations. x = t − sin t, y = 1 − cos t, 0 ≤ t ≤ 2π x = 2t − sin(2t), y = 1 − cos(2t), 0 ≤ t ≤ π (a) Compare the graphs of the two sets of parametric equations in earlier part. When the curve represents the motion of a particle and t is time, what can you infer about the average speeds of the particle on the paths represented by the two sets of parametric equations?
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