Cranberry sorting

We must assume the case where the rotten cranberry loses 90% of its total energy. Dropping from a height of 10 centimeters, it can only bounce up to 1 cm, which is our answer.

$10\times 90\%=\boxed{1}$

LOL 10% of 10 much?

Easy just use EP= m.g.h M and G = K 10-90%= 1

As the berries are dropped from $10cm$ height, the good berries will surely bounce over $10cm$ height... It's given that the rotten berries loss 90% of it's energy... So, it'll not bounce over,

90% of $10cm$ = $10cm \times \frac {90}{100} = 1 cm$

Hence, the required answer is $\fbox {1}$ ...

By the mechanic energy conservation principle, when the object falls, all potencial energy becomes kinetic energy. However, the object loses 90% of its total energy, so we can conservate the energy from the bouncing instant to the moment it reaches the highest height:

0.1(mgH)=mgh ---> 0.1(10^-1)=h ----> h= 1cm.

Potential energy after bouncing will be 0.1 of mgh = mg (0.1)h The height to which they rise is 0.1 10 = 1 cm is the answer.

The cranberry has some gravitational potential energy when it is released. After bouncing, at its new highest point it will have 90% less gravitational potential energy: although some energy was converted to kinetic and back, conservation of energy tells us that none got 'lost' apart from the 90% specified.

For distances that are small relative to the size of the earth, gravitational potential can be approximated by (mass * height * acceleration due to gravity). So losing 90% of its energy means that it loses 90% of its bounce height (mass and gravity are constants).

A rotten cranberry will lose 90% of its energy, so only 10% energy will be left. Energy is directly proportional to the height, which means that 10% energy left will result in only 10% of height reached. Thus, 10% of 10 cm is 1cm

(M V^2)/2=10 (MgH/100) cause 90% was lost during the fall.

so V^2=2g ,by the conservation of energy : mgh=(mV^2)/2 , h=2g/2g=1

By the Law of Conservation of energy applied on the cranberries, we can write Ep = mgh and Ek = Ep , and after they bounce they lose 90 % of their energy. So their energy is 0,1 * Ep = mgx, where x is the minimum height of the wall. 0,1*mgh = mgx => x = 0,1 h = 0,1 * 10cm = 1 cm.

Let the energy at the initial point of drop be = E

As the energy is only with respect to its height , E = m g H (where m is mass of the object g is the acceleration due to gravity & H is the height from ground)

Now as the berry hits the ground and bounces back it loses energy as given n now let energy = E_(2)

e = m g h (h is the new height) Given e = 0.1 E => m g h=0.1 * m g*H

h = 0.1 * 10 = 1 cm

A rotten cranberry loses at least $90\%$ of its energy during a bounce, so it retains no more than $10\%$ of its energy. This means that the cranberry will only bounce at most $10\%$ as high as it was dropped from, so if it is dropped from $10$ cm, it can only bounce up to $10 \cdot 10\% = 1$ cm high. Thus, the minimum wall height is $\boxed{1}$ cm.

The height of the wall must be at least the height of the rotten cranberries that bounce highest, so the height of the wall is the height a cranberry which loses $90$ % of its energy will bounce to. The potential energy of the cranberry is proportional to its height. Therefore, if it is dropped from $10$ cm and it loses $90$ % of its energy, it only has the energy left to reach $10$ % of its initial height, which is $10 \cdot 0.1 = \boxed{1}$ cm.

We can use the ratio principle to do this problem.

We know that the cranberries are dropped from h = 10 cm

If the cranberries are lost at least 90 % of it's energy.... So that's mean that, the cranberries only have 10 % of it's initial energy to bounce.

So, the minimum height in cm of the wall so that no rotten cranberries could ever bounce over it is : 10 % x h = 10 % x 10 cm = 1 cm

mgh/mgh'=100/10 so,h'=h/10=(10/10)cm=1 cm

Since 90% of the energy is lost, 10% of the energy is conserved. Therefore, mgh = (1/10)mgh . By cancelling out the mg, we know that the minimum height that the cranberry can bounce is 1/10 of the original height which is 1/10(10) = 1cm.

As a rotten cranberry will lose 90% of its energy during a bounce,then the minimum height of the wall is $1-\frac {9}{10} \times 10cm=\frac {1}{10} \times 10cm=1cm$

Energy in it = mg10

only 100-90 = 10% energy it will left

so only 10% of 10 cm = 1 cm will be the height

After the bounce, the rotten cranberry loses at least 90% of its energy, and so it can only have at most 10% left. Ten percent of 10 cm is one centimeter. Explanations aside, that's about it.

Potential energy = mass x gravity x height

Since 90 % of energy is lost, 10% is conserved.

10/100 x m x g x 10 cm( before bounce)= m x g x h ( after bounce) Therefore, h= 10/100 x 10 = 1 cm

Seeing that a tenth of energy is consumed, (1/10)(10cm)=1cm

When a berry is dropped from a height h1 total energy of the berry is mgh1.

90% of this energy is lost in one bounce, therefore energy remaining=0.1mgh1.

After bouncing if the berry rises to a height h2 then total energy of the berry is mgh2. According to conservation of energy,

                                                 mgh2=0.1mgh1
                                                   i.e h2=0.1h1

Plug in the value and get the answer.