Max KE of a squirrel jumping from the top of a tree

• Boop de Boop
In summary, the maximum kinetic energy of a squirrel jumping from the top of a tree is dependent on its initial velocity and the height of the tree. The higher the tree and the faster the squirrel's initial speed, the greater the squirrel's potential for maximum kinetic energy upon landing. Factors such as air resistance and the squirrel's body mass may also play a role in determining the maximum kinetic energy.
Boop de Boop

Homework Statement

1. A squirrel jumps horizontally from the top of a 25 m tall tree with a speed of 8 m/s. What is the maximum kinetic energy of the squirrel during its entire trip down to the ground from the top of the tree?
2.If another squirrel of the same mass jumps straight upward from the ground well enough to get 4m off the ground and then falls back to the ground, what is the kinetic energy in the following locations and time:
a)3m above ground, on the way up
b)2m above ground, on the way down
c)1m above ground, on the way down

Pe:mgh
ke:0.5mv^2
pei+kei=pef+kef

The Attempt at a Solution

I know that we have to use the ke initial and add it with the new kinetic energy that is gained during gthe trip in order to calculate total kinetic energy before it hits the ground for prolem 1. But I am really confused and would appreciate guidance. I do not need the answers just help. :)

Last edited by a moderator:
Boop de Boop said:
I know that we have to use the ke initial and add it with the new kinetic energy that is gained during gthe trip in order to calculate total kinetic energy before it hits the ground for prolem 1
So where are you stuck, finding the initial KE, finding the KE gained in the fall, or in adding the two?

I used the kinematic equation vf^2=vi^2+2ad and found final velocity which is 23.74. Then I plugged into ke-)0.5mv^2. I'm confused with kinetic initial. Is it just ke formula but v final is 8

Boop de Boop said:
I used the kinematic equation vf^2=vi^2+2ad and found final velocity which is 23.74. Then I plugged into ke-)0.5mv^2. I'm confused with kinetic initial. Is it just ke formula but v final is 8
That kinetic equation is usually used for one dimensional motion, but here the initial velocity and the acceleration are in different directions.
However, it will give the right result here thanks to Pythagoras; see the later Edit below. Suppose we take that equation and multiply it everywhere by ½m:
½mvf2=½mvi2+mad, where d is the height of the descent and a is g. You can see that this represents
Final KE = initial KE + lost GPE.
I.e. it is the equation for conservation of mechanical work.

Edit: if you want to do it by kinetics rather than work conservation, a more usual path would be to treat the horizontal and vertical separately:
vfx2=vix2+0 (no horizontal acceleration)
vfy2=viy2+2(-d)(-g), where viy=0.
Then you can add these to get the square of the landing speed.

Last edited:
Boop de Boop said:
A squirrel jumps horizontally from the top of a 25 m tall tree with a speed of 8 m/s. What is the maximum kinetic energy of the squirrel during its entire trip down to the ground from the top of the tree?
From energy conservation KEheight+mgh=KEground+0 where KEground is the max. KE

Boop de Boop said:
2.If another squirrel of the same mass jumps straight upward from the ground well enough to get 4m off the ground and then falls back to the ground, what is the kinetic energy in the following locations and time:
From energy conservation
KEi+0=KEheight+mgh ,
During upward journey.
During downward journey
mghmax=mgh+KEheight

Apashanka said:
From energy conservation KEheight+mgh=KEground+0 where KEground is the max. KE
@Boop de Boop seems to understand that (see post #1), but became confused when trying to solve it with SUVAT equations (see post #3).
By the way @Boop de Boop, you meant "kinetic", not "kinematic". Kinematics concerns the geometry of moving systems. See e.g. https://en.m.wikipedia.org/wiki/Kinematics.

1. How do you calculate the maximum kinetic energy of a squirrel jumping from the top of a tree?

The maximum kinetic energy of a squirrel jumping from the top of a tree can be calculated using the formula KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the squirrel, and v is the velocity at which the squirrel jumps.

2. What factors affect the maximum kinetic energy of a squirrel jumping from the top of a tree?

The factors that affect the maximum kinetic energy of a squirrel jumping from the top of a tree include the mass of the squirrel, the height of the tree, and the initial velocity at which the squirrel jumps.

3. How high can a squirrel jump from the top of a tree?

The height a squirrel can jump from the top of a tree depends on several factors, such as the species and age of the squirrel, as well as the height and type of tree. On average, squirrels can jump anywhere from 10-20 feet from the top of a tree.

4. Is the maximum kinetic energy of a squirrel jumping from the top of a tree dangerous?

The maximum kinetic energy of a squirrel jumping from the top of a tree is not considered dangerous, as squirrels have evolved to have strong and agile bodies that can handle the impact of jumping from trees. However, it is important to respect wild animals and give them space to move freely.

5. How does the maximum kinetic energy of a squirrel jumping from the top of a tree compare to other animals?

The maximum kinetic energy of a squirrel jumping from the top of a tree is relatively low compared to other animals, such as birds and mammals. This is due to the small size and weight of squirrels, which limits their jumping capabilities compared to larger animals.

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