MTH254-RecAct-Week3.pdf

# D with no interference when does the ball hit the

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(d) With no interference, when does the ball hit the ground? Where does it hit the ground ? (e) What is the maximum height the ball reached? (3) Two dimensional motion is described by the position vector r ( t ) = x ( t ) , y ( t ) = a ( t - sin t ) , a (1 - cos t ) . The graph of this curve is a cycloid. (a) Find a tangent vector to the cycloid at t = 3 π/ 2 (with a = 1, shown on the right). Draw this tangent vector on the graph of the cycloid. (Note that t = 3 π/ 2 does not mean x = 3 π/ 2.) (b) The parameter range 0 t 2 π produces one arch of the cycloid. Show that the length of one arch of the cycloid is 8 a . (The bicycle wheel has radius a .) Hint: use the trigonometric identity 1 - cos( θ ) = 2 sin 2 θ 2 .

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Math 254 Week 3 Recitation Activity - Fall 2018 Page 2 of 2 (4) Use integration to compute the arc length of the following curve: ~ ( t ) = 2 + 3 t, 1 - 4 t, - 4 + 3 t , 1 t 6 . There is a way to check your answer by computing the arc length by a different method. What is it? (5) An object moves on a trajectory described by ~ r ( t ) = 3 cos t + 2 sin t, - 3 cos t + 2 sin t, 2 sin t , 0 t 2 π. (a) Show that the object moves on a sphere and find the radius of the sphere. (b) Find the velocity and speed of the object.
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• Fall '09
• Hellin
• Trigonometry, Velocity, Manifold, sin t

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