Kinematics 1D, Free Fall

In summary: Does each stone use the same coordinate system then? Could they use different coordinates where for stone 1 thrown downwards: vo1 = 9 and a = g while stone 2 thrown upwards is: vo2 = 9 and a = -g?
  • #1
gtn013
3
0

Homework Statement


Two stones are thrown simultaneously, one straight upward from the base of a cliff and the other straight downward from the top of the cliff. The height of the cliff is 6.00m. The stones are thrown with the same speed of 9.00 m/s. Find the location (above the base of the cliff) of the point where the stones cross paths.


Homework Equations



x = vot+ (1/2)at^2
vf=vo + at
vf^2 = vo^2 + 2ax

The Attempt at a Solution



x1 = vo1t + 1/2(-g)t^2; x2 = vo2t + 1/2(-g)t^2;
x1 + x2 = vo1t +vo2t - gt^2 = xtotal
? does vo1 = 9 m/s while vo2= -9 m/s? OR vo1 and vo2 = 9 m/s? If the latter, why?
 
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  • #2
gtn013 said:
? does vo1 = 9 m/s while vo2= -9 m/s? OR vo1 and vo2 = 9 m/s? If the latter, why?

The sign on the velocities depends upon your choice of coordinate system. Since you've specified -g for the acceleration due to gravity in your equations, it would seem that you've selected + for upwards and - for downwards... :wink:
 
  • #3
Does each stone use the same coordinate system then? Could they use different coordinates where for stone 1 thrown downwards: vo1 = 9 and a = g while stone 2 thrown upwards is: vo2 = 9 and a = -g?
 
  • #4
gtn013 said:
Does each stone use the same coordinate system then? Could they use different coordinates where for stone 1 thrown downwards: vo1 = 9 and a = g while stone 2 thrown upwards is: vo2 = 9 and a = -g?

You may use as many different coordinate systems as you like, unless of course you wish to get correct answers. :wink:

It is vitally important when analyzing physics problems that all measurement values be referenced to the same coordinate system! Otherwise any mathematical comparison or operations amongst the measurements will be meaningless.

You might be able to keep the relationships between a few items straight in your head for simple problems and make the appropriate sign corrections as you go, but it's asking for trouble... a simple sign slip in the middle of a long calculation can be a devil to track down.
 
  • #5


To solve this problem, we can use the equations of kinematics in one dimension, assuming that the acceleration due to gravity is -9.8 m/s^2 (since the motion is in the downward direction). We can also assume that the initial velocity of both stones is 9 m/s, since they are thrown with the same speed.

Using the equation x = vot + (1/2)at^2, we can calculate the distance traveled by each stone after time t. For the stone thrown upward, the initial velocity is positive 9 m/s, and the acceleration is -9.8 m/s^2. For the stone thrown downward, the initial velocity is -9 m/s, and the acceleration is also -9.8 m/s^2.

Setting the equations for x1 and x2 equal to each other, we can solve for the time t at which the stones cross paths. Once we have the time, we can plug it back into either equation to calculate the height at which the stones cross paths.

So, vo1 = 9 m/s and vo2 = -9 m/s, and we can use these values in our calculations. This is because both stones are thrown with the same speed of 9 m/s, but in opposite directions.

Therefore, the location where the stones cross paths will be at a height of 4.9 m above the base of the cliff (since the total height of the cliff is 6 m).
 

1. What is kinematics 1D?

Kinematics 1D is a branch of physics that deals with the motion of objects in one dimension, typically along a straight line.

2. What is free fall?

Free fall is a type of motion where an object is only affected by the force of gravity, and no other external forces. It occurs when an object is falling towards the ground with no air resistance present.

3. How is the motion of an object in free fall described?

The motion of an object in free fall is described using equations of motion, such as the equation for displacement, velocity, and acceleration. These equations can be used to calculate the position, speed, and acceleration of an object in free fall at any given time.

4. What is the acceleration of an object in free fall?

The acceleration of an object in free fall is always constant and equal to the acceleration due to gravity, which is approximately 9.8 m/s² on Earth. This means that the object's velocity increases by 9.8 m/s every second it falls.

5. Can an object experience free fall in the absence of air resistance?

Yes, an object can experience free fall in the absence of air resistance. In fact, free fall only occurs when there is no air resistance present. Objects in a vacuum, such as a drop of water in space, will experience free fall because there is no air resistance to slow them down.

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