Question

A tile is dropped at a height of 12 Meters. The tile has a mass of 2.5kg.
Calculate the final speed of the tile just before it hits the ground

Answer 1

a = dv/dt

v = dy/dt

dt = dv / a = dy/ v

v dv = a dy

Integral [ v dv ]vo--->vf = Integral [ a dy ]y0---> yf

vf^2 - v0^2 = ( 2 ) ( a ) ( yf - y0 )

a = -g

vf^2 - vo^2 = ( 2 ) ( g ) ( y0 - yf )

vf^2 = vo^2 + ( 2 ) ( g ) ( y0 - yf )

vf^2 = ( 0.0 )^2 + ( 2 ) ( 9.807 m/s ) ( 12.0 m - 0.0 m )

vf^ = SQRT [ 235.368 m^2/s^2 ]

vf = 15.34 m/s downward <-------------------------------

The mass and shape of the tile do not matter in this situation of free fall
ignoring air resistance