Falling Cantaloupe - Distance Above Ground

  • Thread starter Thread starter Catchingupquickly
  • Start date Start date
  • Tags Tags
    Falling Ground
AI Thread Summary
A cantaloupe weighing 0.45 kg falls from a height of 5.4 meters and strikes a tree branch at a speed of 6.3 m/s. Using the equation Δh = (v_i^2 - v_f^2) / (2g), the calculated height of the branch is approximately 3.38 meters above the ground. The mass of the cantaloupe is irrelevant to the height calculation. An alternative check suggests the cantaloupe falls about 2 meters in roughly 0.65 seconds, supporting the initial calculation. The conclusion confirms the branch's height as approximately 3.38 meters.
Catchingupquickly
Messages
24
Reaction score
0

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?
 
Physics news on Phys.org
I think so.
 
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##.
 
  • Like
Likes Catchingupquickly
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top