How high is the building?
A physics student with too much free time drops a watermelon from a roof of a building, hears the sound of the watermelon going "splat" 2.5s later. How high is the building? The speed of sound is 340m/s. You may ignore air resistance.
- texasmaverickLv 77 years agoFavorite Answer
The formula the distance of a free falling object is
s = 0.5 * g * t1² (1)
The formula for the distance sound travels is
S = Velocity * t2 (2)
The total time for the mellon to fall and the sound return is T =t1 + t2. T = 2,5
2.5 = t1 + t2 (3)
Equating the formulas for the distance
(0.5 * g * t1²) = 340 * t2 (sound velocity is 340 m/s)
4.9 * t1² = 340 * t2
t2 = (4.9 * t1²) / 340
Substituting the value of t2 into formula (3)
2.5 = t1 + ((4.9 * t1²) / 340)
850 = 340t1 + 4.9t1²
4.9t1² + 340t1 - 850 = 0
using an online quadratic formula calaulator, the roots for t1 are
2.415885683 and -71.8.....
Using the real root, t2 is 2.5 - 2.415885683 = 0.084114317 seconds
This makes the building 0.084114317 * 340 = 28.5988678 n tall
Checking with formula (1)
S = 0.5 * g * t1²
S = 4.9 * 2.415885683²
S = 4.9 * 5.83650.....
S = 28.5988678....
The 2 calculations are the same, so this is your answer.
- az_lenderLv 77 years ago
I'm choosing a method that
evades the quadratic formula.
If the sound were transmitted instantaneously,
the 2.5s would be the time for the melon to fall,
and you'd have h = (1/2)gt^2
= (1/2)(4.9 m/s^2)(2.5 s)^2 = 30.625 m,
and the time for the sound to rise 30.6 m
would be only 0.090 seconds.
So back up and assume the time
for the melon to fall was 2.410 s; then
h = (1/2)gt^2 = 28.46 m, and the time
for the sound to rise is 0.084 s.
If the time to fall were 2.416 s, then
h = (1/2)gt^2 = 28.60 m, and the time
for the sound to rise is 0.08412 seconds.
If the time to fall were 2.41588 s, then
h = 28.5987 m, etc.
Concluding that h = 28.60 meters.
- BrambleLv 77 years ago
Let the height of the building be h
Time to fall = √(2.h/g)
Time for sound of impact to return to student = h/340
Therefore: √(2.h/g)+h/340 = 2.5 which (with g=9.8) solves to give h = 28.6 m
- 7 years ago
Therefore--> distance=speed x time
So... speed=340m/s and time=2.5s
Dist= 340 x 2.5 = 850m
If in doubt use your units. Speed in m/s basically means metres divided by seconds, hence your speed is distance divided by time.
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- Anonymous7 years ago
First,air resistance does not matter in propagation of sound..