There is a spade being held above a flat area of soil. The spade is released and falls vertically. It takes 0.29s for the blade to reach the...

Because it is being held vertically, when it is released
it accelerates due to gravity.  The initial velocity is zero because it is not moving.
The equation to use is:

Vf = Vi + gt where Vf is the
velocity just before it hits the ground, Vi is the initial velocity, g is 9.8 m/s/s, and
t is the time in seconds.

Solving you get:  Vf = 0 + 9.8 *
0.29 = 2.842 m/s

Once the spade hits the ground it starts
slowing down until it comes to a stop. In this case the final velocity is zero, the
initial velocity is the just calculated 2.842 m/s, the distance traveled is 50 mm or
0.050 m, and the rate of slowing (the acceleration is
unknown).

The appropriate kinematic equation is:  Vf^2 =
Vi^2 + 2a(Yf - Yi)

where Vf is the final velocity =
0

Vi is the initial velocity = 2.842
m/s

(Yf - Yi) is the distance traveled = 0.050
m

a is the acceleration you are looking
for.

Solving you get:

0^2 =
2.842^2 + 2a(0.50)

a = -8.077 m/s/s  The minus sign
indicating the spade is slowing down.