Question

A screwdriver

Answer 1

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

$s=ut+\frac{1}{2}at^2\\\Rightarrow h=0t+\frac{1}{2}\times 32.2\times t^2\\\Rightarrow h=\frac{1}{2}\times 32.2\times t^2$

For the sound

Distance = Speed × Time

$\text{Distance}=1100\times (6-t)$

Here, distance traveled by the screwdriver and sound is equal

$\frac{1}{2}\times 32.2\times t^2=1100\times (6-t)\\\Rightarrow 16.1t^2+1100t-6600=0\\\Rightarrow 161t^2+11000t-66000=0$

$t=\frac{-11000+\sqrt{11000^2-4\cdot \:161\left(-66000\right)}}{2\cdot \:161}, t=\frac{-11000-\sqrt{11000^2-4\cdot \:161\left(-66000\right)}}{2\cdot \:161}\\\Rightarrow t=5.55, -73.87$

The time taken to fall down is 5.55 seconds

$h=\frac{1}{2}\times 32.2\times 5.55^2=495.92\ m$

Height of the shaft is 495.92 m

Answer 2

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