timmy falls into a well. The splash happened 5.32s after Timmy began falling. Knowing that sound travels at 340.29m/s. Figure out how deep the well is.

Question

he starts falling and splashes at the bottom of the well 5.32seconds later. how deep is it?

Answer 1

The elapsed time comprises the time of fall and the time for sound to travel:

 

t = t_f + t_s

 

 

The time for falling is determined by the acceleration of gravity and is given by d = ½gt².

 

t_f = √(2d/g)

 

 

The time for sound to travel after splashdown is given  d = v_st. 

 

t_s = d/v_s

 

 

Putting it all together,

 

t = t_f + t_s = √(2d/g) + d/v_s

 

 

(t - d/v_s)² = 2d/g

 

 

t² - 2td/v_s + d²/v_s² = 2d/g

 

 

d² - 2(v_st + v_s²/g)d + v_s²t² = 0

 

 

d = (v_st + v_s²/g) - ½√[4(v_st + v_s²/g)² - 4v_s²t²]

 

 

d = 121 m