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현재 위치

Calculation of the drop height by the time taken to hear the sound of hitting the floor from when it is dropped

작성자 Uploader : 자유낙하 작성일 Upload Date: 2019-06-24변경일 Update Date: 2019-07-15조회수 View : 244

Calculate the height h (m) at which the object is dropped, if the time taken to hear the sound of hitting the floor from when it is dropped is T (s).

The distance of free falling of an object can be expressed as a function of time t (s) as follows.

h = (1/2)*g*t^2

t = (2*h/g)^(1/2)

If the speed at which sound travels in air is v (m/s), then the time ts (s) to travel h (m) is :

ts = h / v

Since the time at which sound is heard from the moment the object is dropped is T = t + ts,

T = t+ts = (2*h/g)^(1/2) + h/v

Substituting by h^(1/2) = x ,

(1/v)*x^2 + (2/g)^(1/2)*x - T = 0

Applying the root formula so that x has a positive value,

x = (v/2)*(-(2/g)^(1/2)+(2/g+4*T/v)^(1/2))

h = x^2 = (v/2)^2*(-(2/g)^(1/2)+(2/g+4*T/v)^(1/2))^2

*** 참고문헌[References] ***

h = (v/2)^2*(-(2/g)^(1/2)+(2/g+4*T/v)^(1/2))^2

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변수명 Variable	변수값 Value	변 수 설 명 Description of the variable

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현재 위치

Calculation of the drop height by the time taken to hear the sound of hitting the floor from when it is dropped

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