Answer to Question #12647 in Mechanics | Relativity for andi

Question #12647
a physics student drops a watermelon from the roof of the building. he hears the watermelon splat 2.50 seconds later. how high is the building? the speed of the sound is 340m/s. ignore air resistance.
Let&#039;s consider the following statement:

T = Tf + Ts,

where T is the total time elapsed from the moment of dropping the watermelon to the moment of hearing the splat (T = 2.5 s), Tf is the flight time of the lemon and Ts is the sound flight time. Let H be the height of a building. Then

H = g&middot;Tf&sup2;/2 ==&gt; Tf = &radic;(2H/g)

and

Ts = H / Vs,

where Vs is the speed of the sound (Vs = 340 m/s).

So,

& radic;(2H/g) + H/Vs = T,

or

H/Vs + &radic;H&middot;&radic;(2/g) - T = 0.

We&#039;ve got a quadratic equation.

& radic;H = ( -&radic;(2/g) &plusmn; &radic;(2/g + 4T/Vs) ) &middot; Vs/2 =

= ( -&radic;(2/9.8) &plusmn; &radic;(2/9.8 + 4&middot;2.5/340) ) &middot; 340/2 = 5.3478 or -158.9441.

So, the height of a building is H = 5.3478&sup2; = 28.5989 m.

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