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

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In summary, the two objects are dropped from a 60 m height with initial velocities of 20 m/s and 15 m/s. Using the formula D= iV * T + a*t^2/2, it was determined that the first object hits the ground after 2 seconds. The distance of the second object at that time is also 10 m.
  • #1
Purpplehaze
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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.


Homework Equations





The Attempt at a Solution

 
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  • #2


What have you done so far? What kinematic equations describe the position of an object as a function of time?
 
  • #3


D= iV * T + a*t^2/2 I think that's the formula to be used.
 
  • #4


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?
 
  • #5


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.
 
  • #6


Would this work? 2(D-iV)/a = t
 
  • #7


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

No, how did you get this?
 
  • #8


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

Done right, you'll end up with a quadratic equation.
 
  • #9


Then how can I isolate t?
 
  • #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 [itex]t^2[/itex]. 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.
 

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

1. What is freefall?

Freefall is the motion of an object falling under the sole influence of gravity. In this type of motion, the object is accelerating towards the ground at a constant rate of 9.8 meters per second squared.

2. How is the distance of a freefalling object calculated?

The distance of a freefalling object can be calculated using the equation d = 1/2 x g x t^2, where d is the distance, g is the acceleration due to gravity, and t is the time in seconds.

3. Why do objects fall at the same rate in freefall?

Objects fall at the same rate in freefall because the acceleration due to gravity is constant and does not depend on the mass or size of the object. This means that all objects, regardless of their mass, will accelerate towards the ground at the same rate.

4. How does air resistance affect freefall?

Air resistance can affect freefall by slowing down the acceleration of an object. As the object falls, it will encounter air molecules that will create a force in the opposite direction of its motion, known as drag. This force will increase as the object's velocity increases, eventually reaching a point where it is equal to the force of gravity, resulting in a constant velocity known as terminal velocity.

5. Can an object's shape affect its freefall distance?

Yes, an object's shape can affect its freefall distance. Objects with larger surface areas will experience more air resistance, which can slow down their acceleration and decrease their freefall distance. On the other hand, objects with smaller surface areas will have less air resistance and may have a longer freefall distance.

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