Answer:
495.92 m
Step-by-step explanation:
Let h be the height of the shaft
t = Time taken by the screwdriver to fall to the ground
Time taken to hear the sound is 6 seconds
Time taken by the sound to travel the height of the shaft = 6-t
Speed of sound in air = 1100 ft/s
For the stone falling
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow h=0t+\frac{1}{2}\times 32.2\times t^2\\\Rightarrow h=\frac{1}{2}\times 32.2\times t^2[/tex]
For the sound
Distance = Speed × Time
[tex]\text{Distance}=1100\times (6-t)[/tex]
Here, distance traveled by the screwdriver and sound is equal
[tex]\frac{1}{2}\times 32.2\times t^2=1100\times (6-t)\\\Rightarrow 16.1t^2+1100t-6600=0\\\Rightarrow 161t^2+11000t-66000=0[/tex]
[tex]t=\frac{-11000+\sqrt{11000^2-4\cdot \:161\left(-66000\right)}}{2\cdot \:161}, t=\frac{-11000-\sqrt{11000^2-4\cdot \:161\left(-66000\right)}}{2\cdot \:161}\\\Rightarrow t=5.55, -73.87[/tex]
The time taken to fall down is 5.55 seconds
[tex]h=\frac{1}{2}\times 32.2\times 5.55^2=495.92\ m[/tex]
Height of the shaft is 495.92 m
