#### Fu-Kwun Hwang

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« on: February 23, 2007, 10:23:39 pm »
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The velocity components of blue curve are Vx,Vy , the velocity components of red curve are Vx,Vy.
What is the relation between Vx,Vy and Vx,Vy

(A) Vx= 2Vx, Vy=2Vy
(B) Vx=Vx, Vy=2Vy
(C) Vx=?2 Vx, Vy= ?2 Vy
(D) Vx=Vx, Vy=?2 Vy

After you have your answer ready, Click the mouse inside the applet region and hit "h" key to see how the curve were set up. You can modified the equations for any motion you want to study. Just enter your forumla into the textfield. (hit "h" will toggle the display mode) Enjoy it!

#### lookang

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« Reply #1 on: September 22, 2008, 09:40:36 am »
Click the following image to view more content:

rememer to hit "h" will toggle the display mode, to see the equations

answer is (C) Vx=?2 Vx, Vy= ?2 Vy

by solving by differentiation

since y1 = 4.t - 2.t^2
dy1/dt = 4 - 4.t

y2 = Math.sqrt(2).4.t - 2.t^2
dy2/dt = Math.sqrt(2).4 - 4.t

realizing when t = 0 gives the same answer as t = end point for vy1 and vy2

vy1 = dy1/dt = 4 - 4.t = 4 - 4.0 = 4
vy2 = dy2/dt = Math.sqrt(2).4 - 4.t =Math.sqrt(2).4 - 4.t = Math.sqrt(2).4 .

therefore vy2 = Math.sqrt(2).vy1

similarly,

x1 = t
vx1 = dx1/dt = 1 = vx1 (constant so at end point is the same)

x2 = Math.sqrt(2).t
vx2 = dx2/dt = Math.sqrt(2)

vx2 = Math.sqrt(2).vx1

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