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**1. Homework Statement**

A shock wave moves away from the center of the explosion, its pressure is decreasing, and its speed tends to a constant value. In the filming of a particular explosion, the following data was obtained:

t(s): 0, 0.02, 0.04, 0.06 ,0.08, 0.1, 0.12, 0.14, 0.16, 0.18, 0.2, 0.22, 0.24, 0.26

R(m):0, 29.4, 45.1, 59.9, 61.7, 72.5, 76.6, 84.4 , 93.3, 103.9, 108.7, 115.6, 121.1, 129.4

where t(s) is time in seconds and R(m) is the radius of the explosion in meters(for example at 0.2 secons the radius of the explosion is 108.7 meters), the questions are:

a)Using the data, determine the time interval in wich the relation for R(t)(see below) is valid

b)Determine the final speed of the shock wave

c)If the shock wave is produced at floor level, then the hemispheric wave would have double energy due to the reflection on the floor than the one that is spherical. Using the above data, determine the total energy released in the explosion

**2. Homework Equations**

the relation for R(t) is : R(t)=1.033E

^{0.2}ρ

^{-0.2}t

^{0.4}where E is the energy released in the explosion, ρ is the density of air, t is the time and R(t) is the radius

**3. The Attempt at a Solution**

For b) I divided the relation by t: R(t)/t=(1.033E

^{0.2}ρ

^{-0.2}t

^{0.4})/t = (1.033E

^{0.2}ρ

^{-0.2})/t

^{0.6}

Then I took the limit of the last expression when t tends to infinity an that limit is 0, so I found that the final speed is 0. Is this correct?

For a) and For c) I dont know how can I find the interval of time in which the relation is valid I dont know how to determine the energy of the explosion, I can´t think of anything so I really would appreciate if you can help me whith the problem, thanks a lot :)