Question

An apple drops from the tree and falls freely. The apple is originally at rest a height H0 above the ground. The ground is covered with 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.

A. Find the speed of the apple just before it enters the grass.

B. Find the acceleration of the apple while it is in the grass.

Answer 1

Here we are gonna use Simple concept of Gravitation,

so the distance travelled in free fall is H0-h(height of apple from ground - height of grass)

Since the apple originally started from rest

We know,

where v is the final velocity, g the accln due to gravity and s the distance travelled and u is the initial velocity = 0

so

ie

so speed of apple just before it enters the grass is

so we know the velocity by which the apple is entering the grass and it slows down at a constant rate which means that the acceleration (a) during this period is constant.

so since

so as final speed is 0 i.e v=0

i.e

so

which is the acceleration of apple while it is in grass