Free Falling Object's Initial Height

In summary, the problem reads: A freely falling object requires 1.50 seconds to travel the last 30 meters before it hits the ground. From what height above the ground did it fall?
  • #1
darkmagicianoc
15
0
The problem reads: A freeley falling object requires 1.50s to travel the last 30.0 m before it hits the ground. From what height above the ground did it fall?

If anyone can please help me with this problem, I would be very grateful. Thank you in advance for your time and effort helping me with this problem!
 
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  • #2
What equations might come in handy here? :smile:
 
  • #3


I am thinking that the Kinematic equations might be useful, but I'm not sure if they could be used, or which ones.
 
  • #4
darkmagicianoc said:
I am thinking that the Kinematic equations might be useful, but I'm not sure if they could be used, or which ones.

Well, how is, in general, initial height, initial velocity, time, acceleration and present height related?

Under the assumption of CONSTANT acceleration, that is..
 
  • #5
Maybe using:

Distance (final) = Distance (initial) + [Velocity(initial)] (time) + .5(Acceleration)(time)^2 to get original velocity, and then subtract (9.8 m/s2)(1s) till hitting zero, n adding that time to the 1.5 s, and then try solving for distance?
 
  • #6
First of all:

Make a list of the KNOWN quantities in that equation, and what is UNKOWN.
 
  • #7
a = 9.8m/s2
xm = 30.0 m
tm = 1.50s
xf = 0.00
xi = ?

where i = initial, f = final, and m = somewhere in between
 
  • #8
So, consider now the interval from the intermediate values to the final values, regarding the intermediate values as "initial" for this particular time, then the only unkown would be the velocity the object had 1.5 seconds prior to hitting the ground.

Agreed?
 
  • #9
Yes, that makes sense.

So now that I know how to get the velocity (intermediate), Do I use that as the new Final velocity, put zero as the initial velocity, solve for time and then the distance (using 30.0 as the final distance) and then add the two distances together?
 
  • #10
:tongue: I think I know what to do now! Thank you for helping me!
 
  • #11
darkmagicianoc said:
Yes, that makes sense.

So now that I know how to get the velocity (intermediate), Do I use that as the new Final velocity, put zero as the initial velocity, solve for time and then the distance (using 30.0 as the final distance) and then add the two distances together?

Just one issue:
Remember in your second part of the problem (after you've found the velocity had at 30m height above the ground), you have TWO unkowns:

The initial height from which the object fell, and the time that has elapsed until you've reached a height of 30meters (and having achieved the solved for velocity).

Final note:
Instead of adding one equation, you might solve the second part by using the relation that relates distance&velocities&time, ignoring to solve explicitly for time.

Therefore, you'll need another equation as well, it is simplest to use the kinematic relation relating velocity&acceleration&time.
 
  • #12
:rofl: Thank you for your help! It worked!
 

What is the formula for calculating the initial height of a free falling object?

The formula for calculating the initial height of a free falling object is h = (1/2)gt^2, where h represents the initial height, g represents the acceleration due to gravity, and t represents the time in seconds.

Is the initial height of a free falling object affected by air resistance?

Yes, the initial height of a free falling object can be affected by air resistance. Air resistance can slow down the speed of the object, resulting in a longer time of free fall, and therefore a greater initial height.

How can we measure the initial height of a free falling object?

The initial height of a free falling object can be measured by using a stopwatch to time the object's fall and then plugging the time into the formula h = (1/2)gt^2. Another method is to use a device such as a photogate timer to measure the time it takes for the object to pass through a light beam, which can then be used to calculate the initial height.

What is the acceleration due to gravity on Earth?

The acceleration due to gravity on Earth is approximately 9.8 m/s^2. This value can vary slightly depending on the location and elevation on Earth, but it is generally accepted as 9.8 m/s^2 for most calculations.

Can the initial height of a free falling object be negative?

Yes, the initial height of a free falling object can be negative. This would indicate that the object was dropped from a height below ground level, or that it was thrown downward with an initial velocity. The formula h = (1/2)gt^2 will give a negative value for h in these cases.

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