Answer:
396.9 meter
Step-by-step explanation:
If a represents the acceleration,
Then according to the question,
a = -9.8 m/s²,
[tex]\frac{dv}{dt}=-9.8[/tex] ( acceleration = change in velocity with respect to time ),
[tex]dv = -9.8dt[/tex]
Integrating both sides,
[tex]v=-9.8t + C[/tex]
When t = 0 seconds, v = 0 m/s,
[tex]0 = -9.8(0) + C[/tex]
[tex]\implies C = 0[/tex]
[tex]\implies v=-9.8t[/tex]
[tex]\frac{dx}{dt}=-9.8t[/tex] ( velocity = change in position with respect to time ),
[tex]dx = -9.8tdt[/tex]
Integrating again,
[tex]x=-4.9t^2 + C'[/tex]
When t = 0 , x = 0 meters,
[tex]0=-4.9(0) + C'\implies C'=0[/tex]
Hence, the final equation that shows the position of the hammer after t seconds,
[tex]x=-4.9t^2[/tex]
If t = 9 seconds,
[tex]x = -4.9(9)^2 = -4.9(81) = -396.9[/tex] ( negative sign shows the fall ),
Therefore, it will fall 396.9 meter in 9 seconds
