Answer:
396.9 meter
Step-by-step explanation:
If a represents the acceleration,
Then according to the question,
a = -9.8 m/s²,
( acceleration = change in velocity with respect to time ),
![dv = -9.8dt](https://tex.z-dn.net/?f=dv%20%3D%20-9.8dt)
Integrating both sides,
![v=-9.8t + C](https://tex.z-dn.net/?f=v%3D-9.8t%20%2B%20C)
When t = 0 seconds, v = 0 m/s,
![0 = -9.8(0) + C](https://tex.z-dn.net/?f=0%20%3D%20-9.8%280%29%20%2B%20C)
![\implies C = 0](https://tex.z-dn.net/?f=%5Cimplies%20C%20%3D%200)
![\implies v=-9.8t](https://tex.z-dn.net/?f=%5Cimplies%20v%3D-9.8t)
( velocity = change in position with respect to time ),
![dx = -9.8tdt](https://tex.z-dn.net/?f=dx%20%3D%20-9.8tdt)
Integrating again,
![x=-4.9t^2 + C'](https://tex.z-dn.net/?f=x%3D-4.9t%5E2%20%2B%20C%27)
When t = 0 , x = 0 meters,
![0=-4.9(0) + C'\implies C'=0](https://tex.z-dn.net/?f=0%3D-4.9%280%29%20%2B%20C%27%5Cimplies%20C%27%3D0)
Hence, the final equation that shows the position of the hammer after t seconds,
![x=-4.9t^2](https://tex.z-dn.net/?f=x%3D-4.9t%5E2)
If t = 9 seconds,
( negative sign shows the fall ),
Therefore, it will fall 396.9 meter in 9 seconds