Ice-cream melting time dilation at what velocity?

[kirsten_2009]

Homework Statement

Velma and Mort have identical 10-minute melting ice-cream cones. How fast must Velma move in order for her 10-minute cone to last 3 times longer than Mort’s, as measured by Mort?

Homework Equations

The Attempt at a Solution

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We have not gotten too in depth into mathematics in my class as it mainly focuses on conceptual understanding and estimates. I looked at a table in my textbook and it says that at 0.9 c there is a time dilation of 2.3 and then it jumps to say that at 0.99 c the time dilation is 7.1 so if Mort observes Velma's ice-cream melt slower by a factor of 3...then shouldn't she be moving slightly faster than 0.9 c and slower than 0.99 c? Would that be a reasonable answer? or is there another way to determine the time dilation? Thanks!

 

[Orodruin]

Apart from looking in a graph of the gamma factor or using the actual formula to derive it (it is not very complicated), interpolating in tables is what you are left with.

 

[phinds]

The math is simple algebra. Look up Lorentz Transform. I don't know Latex or I'd put it here for you. It looks so elegant when written properly and ugly when written with just text symbols. It works out to about .94c

 

[kirsten_2009]

Hello,

Thanks for the reply. I think I would like to give this an algebraic try rather than sticking to my textual description...so...is this the right formula?

T = T₀ / √(1-v²/c²)

If that is the correct formula... is c = speed of light, v= relative speed between two observers (by relative would it just be the difference in speed between Mort and Velma? so, 3?), T= Mort's view of Velma's time? T₀ = 1 ?

 

[phinds]

Yep, that's the one. Just plug in "Pc" for v (Percentage of c) and cancel the "c"s and solve for P with T/T0 = 3