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how to solve functional equation?

How to solve for velocity in the time dilation equation?

  • You are standing still and watching a spaceship fly past. You observe that it takes 2.5 hr for the clocks on the spaceship to advance by 1.0 hr. How fast is the spaceship moving, relative to you? So we have to use the time dilation equation: t= t(knot) / sq. root of 1- (v squared / c squared) I'm just having simple algebra problems with this. I can't seem to figure out how to set the problem up so that I can isolate velocity onto one side of the equation...a little help would be nice. You don't even have to solve it if you don't want. Just help me set up the problem. t = 2.5 hr t(knot) = 1 hr. c(squared) = 9e16 I just need to solve for v BUT I dont' know how to set up the equation

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    Formula and calculator can be found here... http://www.1728.com/reltivty.htm

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First, get rid of the sqrt for a while; so we have T^2 (1 - (v/c)^2) = t^2; where t = 1 hour and T = 2.5 hr. Then (t/T)^2 = 1 - (v/c)^2 and (v/c)^2 = 1 - (t/T)^2 so that v^2 = c^2(1 - (t/T)^2). Now do the sqrt thing. Then v = c sqrt(1 - (t/T)^2) = 3E8 sqrt(1 - (1/2.5)^2) = ? mps the velocity you are looking for. You can do the math.

oldprof

First, get rid of the sqrt for a while; so we have T^2 (1 - (v/c)^2) = t^2; where t = 1 hour and T = 2.5 hr. Then (t/T)^2 = 1 - (v/c)^2 and (v/c)^2 = 1 - (t/T)^2 so that v^2 = c^2(1 - (t/T)^2). Now do the sqrt thing. Then v = c sqrt(1 - (t/T)^2) = 3E8 sqrt(1 - (1/2.5)^2) = ? mps the velocity you are looking for. You can do the math.

oldprof

Formula and calculator can be found here... http://www.1728.com/reltivty.htm

Brandon Penzkover

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