Solving for Time: Dropped Pop Can Reaches the Ground

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In summary, a hot air balloon is rising upwards at a constant velocity of 4m/s. At a height of 4m above the ground, a can of pop is accidentally dropped from the basket. Using the kinematic equation d=1/2 (v2 + v1) t, the time it takes for the can to reach the ground can be found by considering the can's initial velocity of 4m/s upwards, its displacement of -4m (taking into account the direction), and the acceleration due to gravity of 9.8m/s^2. This results in a time of approximately 2 seconds for the can to reach the ground.
  • #1
powerxranger1
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Homework Statement


A hot air balloon is rising upward with a constant velocity of 4m/s. As the balloon reaches a height of 4m above the ground the balloonist accidently drops a can of pop over the edge of the basket. How long does it take the pop can to reach the ground?

V2 = 4m/s [up]
v1 = 0
d = 4m

Homework Equations


d=1/2 (v2 + v1) t


The Attempt at a Solution


I got the anser 2 seconds! Please tell me if i did it correctly
 
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  • #2
Hi powerxranger1,

powerxranger1 said:

Homework Statement


A hot air balloon is rising upward with a constant velocity of 4m/s. As the balloon reaches a height of 4m above the ground the balloonist accidently drops a can of pop over the edge of the basket. How long does it take the pop can to reach the ground?

V2 = 4m/s [up]
v1 = 0
d = 4m

Homework Equations


d=1/2 (v2 + v1) t


The Attempt at a Solution


I got the anser 2 seconds! Please tell me if i did it correctly

No, I don't believe that's right. The initial velocity of the can is 4m/s upwards, like you have, but the final velocity is not given. (The final velocity in this case would be the velocity just before the can touches the ground, so it would not be zero.)

So you know the initial velocity and the displacement (but check the signs!); what else do you know about the can's motion? That will help you choose the best kinematic equation to find the time.
 
  • #3
Hm, I'm not really sure that there is any other information given about the can, since there's only two numbers given. I don't understand how to find another piece of information.
 
  • #4
powerxranger1 said:
Hm, I'm not really sure that there is any other information given about the can, since there's only two numbers given. I don't understand how to find another piece of information.

The can is in free fall; what does that tell you? That will give you the third quantity, and so you can find the time.
 
  • #5
Oh. Does that mean it's just 9.8 m/s?
 
  • #6
powerxranger1 said:
Oh. Does that mean it's just 9.8 m/s?

Yes, that's the right magnitude for the acceleration. (And the units are m/s^2.) Just remember to use the correct signs for the initial velocity, displacement and acceleration when you use them in your equation.
 

1. How can I calculate the time it takes for a dropped pop can to reach the ground?

To calculate the time it takes for a dropped pop can to reach the ground, you can use the formula t = √(2h/g), where t is the time in seconds, h is the height in meters, and g is the acceleration due to gravity (9.8 m/s²).

2. What factors affect the time it takes for a dropped pop can to reach the ground?

The main factors that affect the time it takes for a dropped pop can to reach the ground are the height from which it is dropped and the acceleration due to gravity. Other factors that may have a minor effect include air resistance and the shape and weight of the pop can.

3. How accurate is the calculation for the time it takes for a dropped pop can to reach the ground?

The calculation for the time it takes for a dropped pop can to reach the ground is based on the assumption of a constant acceleration due to gravity and neglects factors such as air resistance. Therefore, the calculated time may not be completely accurate, but it provides a close estimate.

4. Can I use the same formula to calculate the time for objects other than a pop can?

Yes, the same formula can be used to calculate the time it takes for any object to reach the ground when dropped from a certain height. However, the acceleration due to gravity may vary depending on the location and can affect the accuracy of the calculation.

5. Is there a way to measure the time it takes for a dropped pop can to reach the ground experimentally?

Yes, the time for a dropped pop can to reach the ground can be measured experimentally by using a stopwatch or a high-speed camera. The experiment can be repeated multiple times and the average time can be calculated for more accurate results.

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