Calculating Distance and Time for Freely Falling Bodies

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Homework Help Overview

The problem involves two balls: one dropped from a height of 24 m and another thrown upwards from ground level with an initial speed equal to the final speed of the first ball. The task is to determine the point at which the two balls cross paths, considering the absence of air resistance.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss writing expressions for the positions of both balls as functions of time to find their intersection point. There are attempts to calculate the time taken for the first ball to fall and the speed at which it hits the ground.

Discussion Status

Some participants have provided guidance on formulating equations for the positions of the balls, while others express confusion about their calculations, particularly regarding the height and distances involved. There is an ongoing exploration of the problem without a clear consensus on the next steps.

Contextual Notes

Participants mention the need to measure positions from the same reference point and the challenge of equating the distances traveled by both balls to the height of the cliff.

Chiralic
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Homework Statement



A ball is dropped from rest from the top of a cliff that is 24 m high. From ground level a second ball is thrown straight up at the same instand theat the first ball is fropped. The initial speed of the second ball is the same as that with which the fist ball hits the ground. In absense of air resistance, the motions of the balls are just the revers of each other. How far below the cliff do the balls cross paths?

Homework Equations

kinematic equations involving vi, vf, a, x and y and time.



The Attempt at a Solution


I know it takes 2.21 s to fall 24 m, and for ball 2 to reach vi of ball one. Vf1 = vi2= 21.7 m/s

help!
 
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So far, so good. Now write expressions for the position of each ball as a function of time. (Make sure you measure the position from the same point for each.) Then you can solve for where the paths intersect.
 
Sorry, you've completely lost me...I keep getting 24 m with what I'm trying...any other thoughts?
 
Chiralic said:
Sorry, you've completely lost me...I keep getting 24 m with what I'm trying...any other thoughts?
Can you show what you're doing?
 
write the distances traveled by each as a function of time
then add them and equate to the height of the cliff

does this help? or do u need more?
 

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