A cannonball is launched from a point 100 m above ground, at a speed of 20 m/s. This is modelled by the equation $h(t)=-4.9t^2 +20t +100$
The speed of sound (of the cannonball is) 380m/s
If a person sitting directly underneath the cannonball runs as soon as they hear the sound do they escape the cannon?
My main question is "$y=-380x+100$" the correct equation to model the cannon's sound?
The propagation of the sound can be modeled as a wave travelling through a linear medium.
So the front of the sound wave is modeled by $y=-380t+100$ which means, at ground level, the sound can be heard at 0.26315 seconds. But the cannonball reaches ground at around 7 seconds. So the person can escape.