A physics student with too much free time drops a watermelon fromthe roof of a building. He hears the sound of the watermelon going"splat" after a tim

Harlen Pritchard

Harlen Pritchard

Answered question

2021-03-18

A physics student with too much free time drops a watermelon from the roof of a building. He hears the sound of the watermelon going"splat" after a time interval of t
We can ignore air resistance. How high is the building? (The speed of sound is vs. Take the free fall acceleration to be g)

Answer & Explanation

hesgidiauE

hesgidiauE

Skilled2021-03-19Added 106 answers

I'll switch up the notation a little to prevent needing subscripts.
T=t
v=vs
The time it takes to hit the ground:
0=h 122
t1=2hg
the duration of sound propagation
h=vt2
t2=hv
T=t1+t2=2hg+hv
2hg=(Thv)2=T22Tvh+h2v2
This simplifies to
gh22v(v+gT)h+gv2T2=0
We can solve quadratic equations using the quadratic formula and by simplifying.
h=vg(v+gT±v2+2gvT)

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