# How Long Does It Take a Dropped Object to Hit the Ground from a Rising Balloon?

• physics kiddy
In summary: It would be helpful to see where you may have made a mistake. Also, don't forget to include the initial height of the balloon in your calculation.
physics kiddy

## Homework Statement

A balloon is at a height of 81 m is ascending upward with a velocity of 12 ms1. A body of 2 kg weight is dropped from it. If g = 10 ms2, the body will reach the surface of Earth in what time.

## The Attempt at a Solution

I don't think mass is of any importance in this question. Hence, I tried to solve it this way:

Since initial velocity = -u
(s=ut+1/2at^2)

81 = -12t+1/2*10*t^2
Solving, we have t = 42seconds.

However this is not the answer. Please explain how I solve this question.

Hello physics kiddy,

physics kiddy said:

## Homework Statement

A balloon is at a height of 81 m is ascending upward with a velocity of 12 ms1. A body of 2 kg weight is dropped from it. If g = 10 ms2, the body will reach the surface of Earth in what time.

## The Attempt at a Solution

I don't think mass is of any importance in this question. Hence, I tried to solve it this way:

Since initial velocity = -u
(s=ut+1/2at^2)

81 = -12t+1/2*10*t^2
Solving, we have t = 42seconds.

However this is not the answer. Please explain how I solve this question.

I think your signs are messing you up. You can orient your coordinate system however you want, it's up to you. But you have to pick a direction and stick to it consistently. In this case, let's choose upward to be the positive direction, and downward to be the negative direction. Then, the object's initial velocity (when dropped) is *upward*, because it is ascending along with the balloon at +12 m/s.

I have assumed upward to be negative and downward positive to make things easier, however, I am not getting the answer...

physics kiddy said:
I have assumed upward to be negative and downward positive to make things easier, however, I am not getting the answer...

Can you show the steps of your solution in more detail?

I would like to clarify that mass is indeed important in this problem as it affects the force of gravity acting on the body. The equation you used, s=ut+1/2at^2, is correct but it only applies to objects in free fall, which is not the case here since the body is initially moving with a velocity of 12 ms1.

To solve this problem, we can use the equation v=u+at, where v is the final velocity, u is the initial velocity, a is the acceleration (in this case, acceleration due to gravity), and t is the time. We know that the final velocity is 0 m/s since the body will come to a stop when it reaches the surface of the Earth. We also know that the initial velocity is 12 ms1 and the acceleration due to gravity is 10 ms2.

Plugging in these values, we get:

0 = 12 + 10t
Solving for t, we get t = 1.2 seconds.

Therefore, it will take the body 1.2 seconds to reach the surface of the Earth. I hope this helps clarify the solution to the problem. Additionally, as a scientist, it is important to always consider all relevant factors and equations when solving a problem to ensure accuracy.

## 1. What is Kinematics?

Kinematics is the branch of physics that studies the motion of objects, without considering the forces that cause the motion.

## 2. What are the three main types of kinematics problems?

The three main types of kinematics problems are 1-dimensional, 2-dimensional, and projectile motion. 1-dimensional problems involve motion in a straight line, while 2-dimensional problems involve motion in two perpendicular directions. Projectile motion involves motion of an object in a curved path due to the influence of gravity.

## 3. How do you calculate velocity in kinematics?

Velocity is calculated by dividing the change in position (displacement) by the change in time. It is a vector quantity, meaning it has both magnitude and direction.

## 4. What is the difference between average and instantaneous velocity?

Average velocity is the total displacement divided by the total time, while instantaneous velocity is the velocity at a specific moment in time. Average velocity gives a general idea of the object's motion over a period of time, while instantaneous velocity gives information about the object's motion at a specific point in time.

## 5. How do you solve kinematics problems involving acceleration?

To solve kinematics problems involving acceleration, you can use the equations of motion, such as the kinematic equations or the SUVAT equations. These equations relate the variables of displacement, velocity, acceleration, and time. By manipulating these equations, you can solve for the unknown variable in the problem.

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