Falling Cantaloupe - Distance Above Ground

In summary, a cantaloupe with a mass of 0.45 kg falls from a tree house that is 5.4 meters above the ground and hits a tree branch at a speed of 6.3 m/s. Using the equation ##\Delta h = \frac {v_i^2 - v_f^2} {2g}##, the height of the tree branch can be calculated to be approximately 3.38 meters above the ground. This is confirmed by calculating the average speed of the falling object and using the time it takes to reach the final speed.
  • #1
Catchingupquickly
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Homework Statement


A cantaloupe with a mass of 0.45 kg falls out of a tree house that is 5.4 meters above the ground. It hits a tree branch at a speed of 6.3 m/s. How high is the tree branch from the ground?

Homework Equations


## \Delta h = \frac {v_i^2 - v_f^2} {2g} ##

The Attempt at a Solution


Given:

g = 9.80 ## m/s^2 ##
inital velocity = 0
final velocity = 6.3 m/s
mass = 0.45 kg (but here it's a red herring)

## \Delta h = \frac {0 - (6.3 m/s)^2} {(2) 9.80 m/s^2}
\\= \frac {-39.69} {19.6} ##
= -2.025 meters

So 5.4 meters - 2.025 meters = 3.375 or 3.38 meters above the ground.

Am I correct?
 
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  • #2
I think so.
 
  • #3
Catchingupquickly said:

Homework Statement


A cantaloupe with a mass of 0.45 kg falls out of a tree house that is 5.4 meters above the ground. It hits a tree branch at a speed of 6.3 m/s. How high is the tree branch from the ground?

Homework Equations


## \Delta h = \frac {v_i^2 - v_f^2} {2g} ##

The Attempt at a Solution


Given:

g = 9.80 ## m/s^2 ##
inital velocity = 0
final velocity = 6.3 m/s
mass = 0.45 kg (but here it's a red herring)

## \Delta h = \frac {0 - (6.3 m/s)^2} {(2) 9.80 m/s^2}
\\= \frac {-39.69} {19.6} ##
= -2.025 meters

So 5.4 meters - 2.025 meters = 3.375 or 3.38 meters above the ground.

Am I correct?

You could always check by calculating it a different way. For example, here is a quick check:

With gravity at ##9.8 m/s^2## it takes about ##0.65 s## to reach ##6.3 m/s##. If gravity were ##10 m/s^2## it would be ##0.63 s##, so it's a bit more than that.

The average speed when falling from rest is half the final speed, so that's approx ##3.1 m/s##.

##3.1 \times 0.65 \approx 1.95 + 0.06 = 2.01##

So, the object fell about ##2 m##.
 
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Related to Falling Cantaloupe - Distance Above Ground

1. How far can a falling cantaloupe travel above ground?

The distance a falling cantaloupe can travel above ground depends on several factors, such as the initial height from which it was dropped, the angle at which it was dropped, and the air resistance. In general, the maximum distance a cantaloupe can travel above ground is around 2 meters.

2. Does air resistance affect the distance a cantaloupe falls above ground?

Yes, air resistance can significantly affect the distance a cantaloupe falls above ground. As the cantaloupe falls, it experiences air resistance which slows it down. This means that the longer it falls, the less distance it will cover above ground.

3. How does the mass of a cantaloupe affect its distance above ground when falling?

The mass of a cantaloupe does not have a significant effect on its distance above ground when falling. This is because, in a vacuum, all objects fall at the same rate regardless of their mass. In the real world, air resistance may play a role, but the difference in mass between different sizes of cantaloupes is not significant enough to impact the distance above ground.

4. Can a falling cantaloupe reach terminal velocity?

Yes, a falling cantaloupe can reach terminal velocity, which is the maximum speed an object can reach when falling due to the balance between gravity and air resistance. However, due to its relatively low mass and size, a cantaloupe may not reach terminal velocity before hitting the ground.

5. How does gravity affect the distance a cantaloupe falls above ground?

Gravity is the force that pulls objects towards the center of the Earth. As the cantaloupe falls, the force of gravity acts on it, causing it to accelerate towards the ground. This means that the longer it falls, the faster it will be moving and the greater the distance it will cover above ground.

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