Find the speed of an apple before it enters the grass An apple drops from the tr

Question

Find the speed of an apple before it enters the grass

An apple drops from the tree and falls freely. The apple is originally at rest a height H_0 above the top of the grass of a thick lawn, which is made of blades of grass of height h. When the apple enters the grass, it slows down at a constant rate so that its speed is 0 when it reaches ground level. Find the speed of the apple just before it enters the grass. Express your answer in terms of the variables H_0, h, and appropriate constants. Find the acceleration of the apple while it is in the grass. Express your answer in terms of the variables H_0, h, and appropriate constants.

Explanation / Answer

a)
Take verticallu up as positive and down as negative direction
displacement,d = -(Ho-h)
a = -g m/s^2
Vi = 0 m/s
Vf = ?
Use:
Vf^2 = Vi^2 + 2*a*d
Vf^2 = 0 + 2*(-g)*-(Ho-h)
Vf^2 = 2*g*(Ho-h)
Vf = - sqrt (2*g*(Ho-h))
Answer: - sqrt (2*g*(Ho-h))
Try now

b)
For grass
a =?
Vi = - sqrt (2*g*(Ho-h))
Vf = 0
d = -h

use:
Vf^2 = Vi^2 + 2*a*d
0 = 2*g*(Ho-h) + 2* (a)*(-h)
a = g*(Ho-h) /h
Answer: g*(Ho-h) /h

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