Hot-air balloon (kinematics question)

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In summary: d(t) = d0 + v0 t d0 is the initial displacementv0 is the initial velocitya is the constant acceleration
  • #1
Sean1218
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Homework Statement



A hot-air balloon is rising upward with a constant velocity of 4.0 m/s. As the balloon reaches a height of 4.0 m above the ground, the balloonist accidentally drops a can of pop over the edge of the basket. How long does it take for the pop can to reach the ground?

Homework Equations



d = v2t - 1/2at^2
other uniform acceleration equations

The Attempt at a Solution



Tried a few different things, but nothing seems to work out. I'm not sure if the pop can starts at v1 = 0 m/s or at v1 = 4.0 m/s because of the rising balloon. It falls from 4.0 m and gravity is -9.8 m/s^2.

That's 4 values, but which of the 4 do I use? I didn't get the right answer from just plugging them in, so I'm not sure what else I can do.
 
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  • #2
Sean1218 said:

Homework Statement



A hot-air balloon is rising upward with a constant velocity of 4.0 m/s. As the balloon reaches a height of 4.0 m above the ground, the balloonist accidentally drops a can of pop over the edge of the basket. How long does it take for the pop can to reach the ground?

Homework Equations



d = v2t - 1/2at^2

Just to eliminate potential problems, in the velocity term, do you mean v2 t, (v2)t, or something else? The equation is either incorrect as written or at least confusing.
This should be an equation for displacement d(t) as a function of:

1. time, t
2. displacement at t=0, d0
3. velocity at t=0, v0
4. acceleration, a.

Try to find the appropriate equation. It's close to the one that you wrote.

other uniform acceleration equations

The Attempt at a Solution



Tried a few different things, but nothing seems to work out. I'm not sure if the pop can starts at v1 = 0 m/s or at v1 = 4.0 m/s because of the rising balloon. It falls from 4.0 m and gravity is -9.8 m/s^2.

That's 4 values, but which of the 4 do I use? I didn't get the right answer from just plugging them in, so I'm not sure what else I can do.

What was the velocity of the can before it was dropped?
 
  • #3
Sorry, meant v2 as in velocity #2.

d = v#2(t) - 1/2at^2 where v#2 = 0, d = 4, a = -9.8, solve for t

if I do it with v#1 instead (v#1 = 4.0), I still don't seem to get the right answer. I must just be plugging in the wrong values, but I've tried everything I can think of.

and the velocity of it before it was dropped was 4.0 m/s, so I guess that'd be v#1, yea.
 
  • #4
I told you to find a more general equation, since you're having trouble identifying how to plug the information given into the equation that you're using. Find the most general equation for displacement at constant acceleration (in your notes or text) and identify the initial and final values that you need to put in.
 
  • #5
i thought that was what I did :confused:
 
  • #6
It's not, the most general equation is

d(t) = d0 + v0 t + (1/2) a t2,

where

d(t) is the displacement after the time t
d0 is the displacement at t=0
v0 is the velocity at t=0
a is the constant acceleration.

It's conventional to measure displacement as increasing in the vertical direction. The signs of the initial velocity and acceleration must be identified consistent with that convention.

Try identifying all of the quantities in the equation above in terms of the information given.
 

Related to Hot-air balloon (kinematics question)

What is a hot-air balloon?

A hot-air balloon is a type of aircraft that uses a large balloon filled with heated air to lift it off the ground. The heated air inside the balloon is less dense than the colder air outside, allowing it to rise and carry the balloon and its passengers with it.

How do hot-air balloons move?

Hot-air balloons move by utilizing wind currents and changes in altitude. By adjusting the temperature inside the balloon and using the wind to navigate, pilots can control the direction and speed of the balloon.

What is the maximum altitude a hot-air balloon can reach?

The maximum altitude a hot-air balloon can reach depends on several factors, such as the size and weight of the balloon, the weather conditions, and the experience and skill of the pilot. On average, hot-air balloons can reach altitudes of 3,000 to 5,000 feet, but some specialized balloons have been known to reach heights of over 20,000 feet.

How long can a hot-air balloon stay in the air?

The duration of a hot-air balloon flight depends on the amount of fuel and the weather conditions. On average, a hot-air balloon can stay in the air for 1-2 hours, but some balloons have been known to stay afloat for several hours or even days with the use of specialized equipment and techniques.

Is hot-air ballooning safe?

As with any form of air travel, there are risks associated with hot-air ballooning. However, with proper training, maintenance, and adherence to safety protocols, hot-air ballooning is generally considered a safe activity. It is important to always follow the instructions of the pilot and be aware of any potential hazards or changes in weather conditions.

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