Free Fall Equations on hot air balloon

In summary, a hot-air balloon descending at a rate of 2.0 m/s has a passenger who drops a camera from a height of 45m. Using the equation d = v1*t + (1/2)at^2, the time it takes for the camera to reach the ground can be calculated by isolating t using the quadratic formula. The velocity just before it lands can also be calculated using the given information and the equation for change in displacement.
  • #1
matace50
3
0

Homework Statement



A hot-air balloon is descending at a rate of 2.0 m/s when a passenger drops a camera. If a camera is 45m above the ground when it is dropped, (a) how long does it take for the camera to reach the ground(b) what is the velocity just before it lands? Let upward be the positive direction for this problem.


Homework Equations


I have to use either 2a x change in displacement= final velocity^2 - initial velocity^2 or
change in displacement= 1/2a x t^2 + initial velocity x change in time

a = acceleration t= time ^2= squared x= multiply

The Attempt at a Solution



I think i somehow have to rearrange the equation to isolate t but i have no idea how. Can anyone help
 
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  • #2
For the first part, use the equation:

d = v1*t + (1/2)at^2

careful about signs... decide first if you want upward to be positive, or downward to be positive...
 
  • #3
I see, but the problem doesn't give me time. I plugged everything in, but i still can't seem to get time.

(just started physics 2 weeks ago so I am kind of confused)
 
  • #4
matace50 said:
I see, but the problem doesn't give me time. I plugged everything in, but i still can't seem to get time.

(just started physics 2 weeks ago so I am kind of confused)

You have to use the quadratic formula to solve for time.
 
  • #5
Ok now i understand. Thanks
 

1. What is the equation for calculating the free fall time of a hot air balloon?

The equation for calculating the free fall time of a hot air balloon is 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. How do you calculate the velocity of a hot air balloon during free fall?

The equation for calculating the velocity of a hot air balloon during free fall is v = gt, where v is the velocity in meters per second, g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds.

3. Can the weight of the hot air balloon affect its free fall time?

No, the weight of the hot air balloon does not affect its free fall time. The free fall time is solely dependent on the height and acceleration due to gravity.

4. How does the temperature affect the free fall equations for a hot air balloon?

The temperature does not directly affect the free fall equations for a hot air balloon. However, temperature can affect the density of the air, which can impact the lift and descent of the balloon.

5. Is there a maximum height that a hot air balloon can reach during free fall?

Yes, there is a maximum height that a hot air balloon can reach during free fall. This is known as the terminal velocity, which is the maximum velocity that an object can reach when falling due to the balance of air resistance and gravity. The exact height will vary depending on factors such as the weight and size of the balloon, as well as air density.

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