Let r(t) = (t, 3 cos(t), 3 sin (t)). Find the arc length of the space curve over
ID: 2880823 • Letter: L
Question
Let r(t) = (t, 3 cos(t), 3 sin (t)). Find the arc length of the space curve over the interval [0, 2 pi]. Describe the curve. Let y = 4x^2 - 1 be a plane curve. Find the curvature at x = 3. Find the radius of curvature at x = 3. A golf ball is hit from the ground, after which there is no wind resistance or other force beyond Earth's gravity acting on the ball. The initial velocity is 100 feet per second and the ball is hit at an angle of 30 degree with respect to horizontal. How far does the ball travel before hitting the ground? What is its maximum height?Explanation / Answer
24) y = 4x2
b) radius of curvature = [1 + (y')2]3/2 / y''
= [1+ (8x)2]3/2 / 8
Rx=3 = [1+ 476]3/2 /8 = 4773/2 /8 = 1302.22
a) k = 1/R = 1/1302.22 = 7 * 10-4
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