I to find the distance of the freefalling objects when one hits the ground.

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Homework Help Overview

The problem involves two objects dropped from a height of 60 m, one with an initial velocity of 20 m/s and the other with 15 m/s. The goal is to determine the distance of the objects when the first one hits the ground, assuming no air resistance.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the appropriate kinematic equations to describe the motion of the objects. There are attempts to apply the equation D = iV * T + a*t^2/2 to find the time it takes for the first object to reach the ground. Questions arise about isolating variables and the implications of using different values for acceleration due to gravity.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the equations and the implications of initial velocities. Some guidance has been offered regarding the use of the quadratic formula and the need to set up equations for both objects.

Contextual Notes

There is a mention of whether the value of g can be approximated to 10 m/s² for simplification. Participants are also considering the implications of having two different initial velocities leading to two distinct quadratic equations.

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Homework Statement


The two objects are dropped from 60 m height. One is dropped having an initial velocity of 20m/s and another with 15 m/s. What is the distance of the objects when the first one hits the ground if there is no air resistance.


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The Attempt at a Solution

 
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What have you done so far? What kinematic equations describe the position of an object as a function of time?
 


D= iV * T + a*t^2/2 I think that's the formula to be used.
 


Purpplehaze said:
D= iV * T + a*t^2/2 I think that's the formula to be used.
Good. So how can you apply this to solve for the time it takes for the 20 m/s object to reach the ground?
 


Purpplehaze said:
D= iV * T + a*t^2/2 I think that's the formula to be used.

Plugin the values for first object and calculate t.
 


Would this work? 2(D-iV)/a = t
 


Purpplehaze said:
Would this work? 2(D-iV)/a = t

No, how did you get this?
 


Purpplehaze said:
Would this work? 2(D-iV)/a = t
No.

Done right, you'll end up with a quadratic equation.
 


Then how can I isolate t?
 
  • #10
  • #11


60=20t + 4.9t^2
 
  • #12


Purpplehaze said:
60=20t + 4.9t^2

Are you allowed to use g=10 m/s^2? That would make calculations a lot easier.
 
  • #13


You have two different objects, with two different initial velocities, each involving t^2. Once you put the initial velocities in, you will have two different quadratic equations. What are those equations?
 
  • #14


Purpplehaze said:
60=20t + 4.9t^2
Good. Now you can put it into standard form and solve it using the quadratic formula (or using whatever method you like).
 
  • #15


I got 2 as T for the first one.
 
  • #16


Purpplehaze said:
I got 2 as T for the first one.
Good!

Now see if you can figure out where the other object (the one thrown with the slower speed) is at that time. Use the same formula, but with different data.
 
  • #17


Ok I got the answer, the distance is 10.
Thanks a lot.
 

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