Finding the Initial Speed of a Falling Object Using Kinematic Equations

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Homework Help Overview

The problem involves two chestnuts dropped from a height, with the first falling a certain distance before the second is thrown down. The objective is to determine the initial speed of the second chestnut so that both reach the ground simultaneously. The subject area pertains to kinematics and motion under gravity.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the timing of the first chestnut's fall and how to relate it to the second chestnut's initial speed. There are attempts to clarify the time taken for the first chestnut to fall a specific distance and how that affects the second chestnut's motion.

Discussion Status

Some participants have provided guidance on focusing on the time taken for the first chestnut after it has fallen 2.5 m, suggesting that this time should be used to determine the conditions for the second chestnut. There is ongoing exploration of how to apply the kinematic equations to find the initial speed of the second chestnut.

Contextual Notes

Participants express confusion regarding the application of kinematic equations and the specific values to use for the variables involved. There is an acknowledgment of the complexity of the problem and the need for clarity on the setup and assumptions.

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Homework Statement


Sitting on a tree branch 10 m above ground. Drop chestnut 1. When chestnut 1 has fallen 2.5 m, I throw a second chestnut straight down.

What is the initial speed of chestnut 2, if they are to both reach the ground at the second time
??

Homework Equations




X=Xo + Vo t + 1/2 at2

a=g
For chestnut 1 v=0
X=1/2gt^2

The Attempt at a Solution



So i got the first chestnuts time, which was
t=(2x/g)^1/2 = 1.4 seconds.

The problem I'm having now is what to do next. Am I supposed to find chestnut 1's time at 2.5? I'm so confused... thanks for helping =)
 
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Instead of finding the time 't' it takes Chestnut 1 to reach the ground from start to finish, find out how long it takes from the time it has fallen 2.5m (i.e. x=7.5m)until it hits the ground. Call this time 't1'

Then, Chestnut 2's velocity must satisfy the condition that it causes the nut to reach the ground in that same amount of time = 't1'.
 
How much time chestnut takes to fall through 2.5 m?
Total time - the above time = the time taken by chestnut 2 to reach the ground.
 
Saladsamurai said:
Instead of finding the time 't' it takes Chestnut 1 to reach the ground from start to finish, find out how long it takes from the time it has fallen 2.5m (i.e. x=7.5m)until it hits the ground. Call this time 't1'

Then, Chestnut 2's velocity must satisfy the condition that it causes the nut to reach the ground in that same amount of time = 't1'.

ok, so i did that, and i got 1.2365 seconds.

so that, and now should i use that time in the X=Xo + Vo t + 1/2 at^2 ?

what should I put for X and Xo?


Sorry, I've just been stuck on this question forever lol.
 

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