# Velma and Mort's ice cream is melting special relativity problem. Help please.

## 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?

## 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!

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Orodruin
Staff Emeritus
Homework Helper
Gold Member
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
Gold Member
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

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