# How high is the tree branch(conservation in energy/kinematics)

• supernova1203
In summary, the first part of the conversation involves calculating the speed of a 2 kg watermelon falling from a treehouse 5.4 m above the ground. The resulting speed is 10.28 m/s. The second part involves finding the height of a tree branch where a 0.45 kg cantaloupe hits at a speed of 6.3 m/s. By using the equation v1^2 - v2^2/2g = Δd, the height is determined to be 2.025 m from the branch to the ground.
supernova1203

## Homework Statement

45a)
A watermelon with a mass of 2 kg falls out of a tree house that is 5.4 m above the ground. What is the speed of the watermelon just before it hits the ground.
(this part i have solved)

mass = 2kg
Δd= 5.4m
v=?

v1^2 =v2^2+2gΔd

v1^2=0+2gΔd

=0+2(9.8)(5.4)

v1^2=√105.84

v1^2=10.28 m/s

Now on to the part i didnt quite get.

45b) A cantaloupe with a mass of 0.45kg falls out of the other side of the tree house. It hits a tree branch at a speed of 6.3 m/s. How high is the tree branch from the ground?

v1^2 =v2^2+2gΔd

v1^2-v2^2/2g=Δd

## The Attempt at a Solution

45b)

v1=0m/s

v2=6.3m/s

mass = 0.45 kg

v1^2-v2^2/2g=Δd

v1^2-v2^2/2g=Δd

6.3^2-0/2g=Δd

6.3^2/2(9.8)=Δd

6.3^2/19.6=Δd

39.69/19.6=Δd

2.025m = Δd

thats the height i got, if it is not correct, can someone show me how to get the right height? or better yet get the right height and i can analyze and figure out how you got the right height?

Hi supernova1203. That would be the height from the branch to the treehouse, the question asks for the height of the branch from the ground.

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Last edited by a moderator:
Sleepy_time said:
Hi supernova1203. That would be the height from the branch to the treehouse, the question asks for the height of the branch from the ground.

Tell me how did you come to that conclusion?

ah...so in order to get the height from the branch to the ground, i would have to subtract the 2 heights...max height and the 2nd height i got for part B of the question?

" A cantaloupe with a mass of 0.45kg falls out of the other side of the tree house. " The tree house is 5.4m above the ground from a), so I think by other side of the tree house just means it is dropped from the same height as in a). And yes that is the answer

## 1. How is the height of a tree branch related to conservation of energy?

The height of a tree branch is related to conservation of energy through the principle of potential energy. As an object is lifted to a higher position, its potential energy increases, and this energy is conserved as it falls back down due to gravity. Therefore, the height of a tree branch is directly related to the conservation of energy.

## 2. How does kinematics play a role in determining the height of a tree branch?

Kinematics is the study of motion and its causes, and it plays a crucial role in determining the height of a tree branch. By using kinematic equations, we can calculate the height of a tree branch by measuring the time it takes for an object to fall from the branch and its initial velocity.

## 3. What factors affect the height of a tree branch in relation to conservation of energy and kinematics?

The factors that affect the height of a tree branch in relation to conservation of energy and kinematics include the mass of the object falling from the branch, the initial velocity of the object, and the height of the branch itself. Other factors such as air resistance and the presence of other objects may also have an impact.

## 4. Can the height of a tree branch be determined accurately using conservation of energy and kinematics?

Yes, the height of a tree branch can be determined accurately using conservation of energy and kinematics. However, it is important to take into account any external factors that may affect the results, such as air resistance or the shape of the object falling from the branch.

## 5. How can the measurement of the height of a tree branch using conservation of energy and kinematics be useful?

The measurement of the height of a tree branch using conservation of energy and kinematics can be useful in a variety of ways. It can help us understand the relationship between energy and motion, as well as provide valuable information for engineering and construction projects. It can also be used to estimate the height of other objects or structures that cannot be measured directly.

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