Gravity Sound

Time taken by the helmet reach ground= $t=\sqrt { \frac { 2s }{ a } }$ , where $s\longrightarrow distance\\ t\longrightarrow time\\ a\longrightarrow acceleration$

$\Longrightarrow t=4\quad seconds$ .

The sound is heard by construction worker after 4.23 s ,

So time taken by sound to reach construction worker= 4-4.23=0.23 s

Speed of sound= $\frac { 78.4 }{ 0.23 }$ = $\boxed{340.87}m/s$

Knowing the height is 78.4 meters and the gravitational constant on Earth as 9.8 meters/second^2, we can use the distance formula to find the time it took the hat to hit the ground as :

D = 1/2 * a * t^2

78.4m = 1/2 * 9.8 m/s^2 * t^2

16 = t^2

t = 4 sec

Thus if it took the total time of the hat to fall and the sound to travel back up, we can find that it took .23 seconds for the sound to travel the distance of 78.4 meters, so to find speed:

Speed = d/t = 78.4/.23

S = 340.8696 *

*to four decimal places

h = u t + 1/2 *g t ^ 2

On solving... t^2 = 16 t^2 = 4

Time= 4.23-4=0.23 S=D/T

Speed= 78.4/0.23

Speed = 340.8695

s=1/2 at^2 so t=4 which is the time to hit the ground. 4.23-4.0 is the time for the sound to travel back to the worker 78.4/.23 = 340.8695

Using, s=ut+1/2at^2 78.4=0+1/2×9.8(t)^2 t=4seconds Time taken by sound to reach the worker=4.23-4=0.23 Speed of sound=78.4÷0.23=340.86

Easy. The speed of sound in air is always 343.2 Meters/Second. Scrubs, memorize some stuff already.