# 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 soil.Calculate the speed. The spade penetrates 50mm...

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 soil.

Calculate the speed.

**The spade penetrates 50mm into the soil. Calculate the average acceleration of the spade in the soil.**

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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.

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