# Sandbag Dropped from Moving Balloon

• Lycouras
In summary, a hot air balloon traveling upwards at a constant speed of 10 m/s has a passenger who drops a small sandbag from a height of 40 m. Using the equation v1=x0+v0Δt+0.5aΔt2, with known values of a=-9.81 m/s2, x0=40 m, v0=0 m/s, and v1=?, the time it takes for the sandbag to fall to the ground is approximately 2.86 seconds. The initial velocity of the sandbag is the same as the velocity of the balloon. The quadratic formula is used to solve for time, and the negative answer is omitted.
Lycouras

## Homework Statement

Hey guys, I'm struggling on the following question:

Consider a hot air balloon traveling upwards at a constant speed of 10 m/s. A passenger drops a small sandbag over the side of the balloon when the balloon was 40 m above the ground. For how long does the sandbag stay in the air before falling to the ground?
Known:
a=-9.81 m/s2
x0=40 m
x1=0 m
v0=0 m/s
v1=?
t=?

## Homework Equations

v1=x0+v0Δt+0.5aΔt2

## The Attempt at a Solution

0=40+0.5(-9.8)Δt2
-40=-4.9Δt2
8.16=Δt2
Δt2=±2.86

Since time cannot be negative, it takes 2.86 seconds, is this correct? Thanks in advance.

Lycouras said:
Consider a hot air balloon traveling upwards at a constant speed of 10 m/s.
...
v0=0 m/s

Since the balloon is moving upwards and the sandbag was dropped from the balloon, the initial velocity of the sandbag is the same as the velocity of the balloon. Other than that, you did everything right.

So from there you use the quadratic formula to solve for t, then again omit the negative answer? Thank you!

correct

Yes, your solution is correct. The sandbag will take approximately 2.86 seconds to fall to the ground. This can be found by using the equation v1=x0+v0Δt+0.5aΔt2 and solving for Δt. It is important to note that this is an approximation since air resistance and other factors may affect the actual time it takes for the sandbag to fall.

## 1. How does the speed of the balloon affect the impact of the sandbag?

The speed of the balloon does not directly affect the impact of the sandbag. The impact of the sandbag is determined by the force of gravity and the height from which it is dropped. However, the speed of the balloon can affect the accuracy of the drop and the location where the sandbag will land.

## 2. Will the weight of the sandbag affect its impact?

Yes, the weight of the sandbag will affect its impact. The heavier the sandbag, the greater the force of gravity acting on it, resulting in a stronger impact upon landing. This is known as the weight-force relationship.

## 3. What factors can influence the trajectory of the sandbag?

The trajectory of the sandbag can be influenced by several factors, including the wind speed and direction, the shape and weight of the sandbag, and the height from which it is dropped. Other environmental factors, such as air density and temperature, may also play a role in the sandbag's trajectory.

## 4. How can the sandbag's impact be measured accurately?

The impact of the sandbag can be measured accurately using various tools such as a force sensor, accelerometer, or high-speed camera. These devices can measure the force of impact, the velocity of the sandbag, and the distance it travels upon landing, providing precise data for analysis.

## 5. What practical applications can be derived from studying the sandbag dropped from a moving balloon?

Studying the sandbag dropped from a moving balloon can have various practical applications, such as understanding the effects of gravity and air resistance on falling objects, predicting the trajectory of projectiles, and improving the accuracy of airdrop operations in fields like military and disaster relief. This experiment can also help in designing safer and more efficient parachutes and other devices that utilize air resistance for controlled descent.

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