Answer: t = 0.878s
Explanation: Dear big brain
since your temperature decreases linearly, you can assume that your velocity should behave linearly too. Here this isn't exactly the case (cfr. formula). But there's another way to prevent endlessly boring calculus. Use the principle of interpolation. (x/v_surface + x/v_top)/2 = t.
This answer won't be exactly the same, but it's a quite good approx. You can use this eqation, hence you don't use large distances.
We have that for the Question it can be said that time it will take sound to rise and the sound travel horizontally in this same time interval is
a)t=0.8secs
b) d=275m
From the question we are told
The air temperature over a lake decreases linearly with height after sunset, since air cools faster than water. The mean molar mass of air is M=28.8×10−3kg/mol.
The questions are:
Generally the equation for the Speed of sound is mathematically given as
Speed
[tex]v=\frac{rRT}{M}[/tex]
Therefore
[tex]v =\sqrt{1.4*8.31*301.15}{28.8*10^{-3}}\\\\v=349m/s[/tex]
Where at 8C
[tex]vf =\sqrt{1.4*8.31*281}{28.8*10^{-3}}\\\\vf=337m/s[/tex]
Using Newton's equation
[tex]V^2=u^2+2as[/tex]
Therefore
[tex]337^2=349^2-2a(280)\\\\a=14m/s^2[/tex]
Using Newton's equation
[tex]t=\frac{v-u}{a}\\\\t=\frac{349-337}{14}[/tex]
t=0.8secs
b)
Generally the equation for the distance is mathematically given as
d=vt
d=337*0.826
d=275m
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