A flowerpot is knocked off a balcony from a height d above the sidewalk as shown

Question

A flowerpot is knocked off a balcony from a height d above the sidewalk as shown in the figure below. It falls toward an unsuspecting man of height h who is standing below. Assume the man requires a time interval of t to respond to the warning. How close to the sidewalk can the flowerpot fall before it is too late for a warning shouted from the balcony to reach the man in time? (Use any variable or symbol stated above along with the following as necessary: v for the speed of sound, and g for gravitational acceleration.)

Explanation / Answer

let the closest distance be L

time taken by sound to reach man T = (d-h)/v

T + delta t = time taken by flowerpot to reach mans head

  (d-h)/v + t = sqrt(2*(d-h)/g) - sqrt(2*(d-L)/g)  

sqrt(2*(d-L)/g) = sqrt(2*(d-h)/g) - (d-h)/v - t

d- L = 0.5g * (sqrt(2*(d-h)/g) - (d-h)/v - t)

L = d - 0.5g * (sqrt(2*(d-h)/g) - (d-h)/v - t)

Answer

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