Question

Le Problem 3.3 The motion of a particle is defined by the equations x=(4cos -2) (2 - cos act) and y =(3 sin TI)/(2 - cos al), where x and y are expressed in feet and / is expressed in seconds. Show that the path of the particle is part of the ellipse shown, and determine the velocity when (a) / -0. (b)/ 1/3 s, (c) 1 = 1 s.

Answer 1

4 Costit -2 - asinkit 2 -costit 3 sinnt 2 -Costit are given and they form ellipse from toom ost 52 of and half ellipse from on room osts Earl velocity = x + y a re [ce-count) (-UIT Sinit)]- Cucart --> (sin txu) (2-Costit) 4 Contit sint & lisinat Sinttorit -8T Sintit at 4 T (2-cant) - 6Ti Sintit (2-count) X2-m) - an x F S +). (2-cart ² 67 Costit (311 COPT + 3a sinnt) 3T (2 costit : 72-cart (2-cant) GT 3 9 4 1)

At to, 21 At t1, At t-% 0 g - 31 s) velocity - 2 x = 0, y = IT , - velocity - 1 % -7,255, ý 30 22 velocity- 7.255