Question

A wrench is dropped by a worker at a construction site.four seconds later the worker hears it hit the ground below. how high is the worker above the ground? (the velocity of sound is 100 ft/sec and the distance the wrench falls as a function of time is s=16t^2)

Answer 1

s = 16 t²      t = √(s/16)        velocity of sound 1100ft/sec

time duration for wrench to hit the ground t1 = √ (s / 16 )  = √s / 4  sec

Time duration for sound to reach the workers' ears = t2 = s / 1100  sec

t1 + t2 = 4 sec

√s / 4 + s/1100 = 4        0.25 x + 0.00091 x² - 4 = 0          if x = √s

Δ = 0.25² + 4*4*0.00091 =  0.07706
 x = (-0.25 +- 0.2776) / 2 * 0.00091  =  - 292.7  or 15.163

s = x² = 229.92   ft    taking the positive value √s = 15.163