# Calculating Time for an Object to Fall in One Dimension

• ShamTheCandle
In summary, the conversation discusses a problem involving a hot air balloon and a dropped compass. The balloon is moving at a constant speed of 2.50 m/s and the compass is dropped from a height of 3.00 m. The formula for solving the problem is mentioned and there is a discussion about the initial velocity of the compass. It is determined that the initial velocity of the compass is 2.5 m/s in the upward direction. The conversation ends with the person thanking everyone for their help.
ShamTheCandle
Hi. I am new to Physics Forums. The following problem is from Physics 6th Edition by Cutnell/Johnson.

A hot air balloon is rising upward with a constant speed of 2.50 m/s. When the balloon is 3.00 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground?

I tried to solve this question by using formula below:

$$h=v_0t+\frac{1}{2}at^2$$

However, I am not sure what is the value of $$v_0$$. Is it zero or 2.50 m/s?

Hi

Vo will be 2.5 m/s in the direction the balloon is moving. If it wasn't then if you where in a moving car and you threw a ball it would fly to the back of the car at the speed the car is moving.. and that don't happen :)

If the balloonist is holding it in his hand, the instantaneous initial velocity of the compass at the time of release is zero with respect to him. Now the balloonist is moving with respect to the ground, so the initial velocity of the compass with respect to the ground is ...

Hi ShamTheCandle,
Welcome to PF.
Before dropping, the compass is moving up with the balloon. So its initial velocity is 2.5 m/s upward. Here displacement and g are in the down ward direction. While substituting in the formula take care about the signs

Thanks all! I appreciate your help.

## 1. What is kinematics in one dimension?

Kinematics in one dimension is a branch of physics that studies the motion of objects along a single axis, without considering the forces that cause the motion.

## 2. What is displacement?

Displacement is the change in position of an object from its initial position to its final position. It is a vector quantity and is measured in units of length (meters, feet, etc.).

## 3. How is velocity defined in kinematics?

Velocity is the rate of change of displacement with respect to time. It is a vector quantity and is measured in units of length per time (m/s, ft/s, etc.).

## 4. What is the difference between speed and velocity?

Speed is the rate of change of distance with respect to time, while velocity is the rate of change of displacement with respect to time. Speed is a scalar quantity and velocity is a vector quantity.

## 5. How is acceleration calculated in kinematics?

Acceleration is calculated as the rate of change of velocity with respect to time. It is a vector quantity and is measured in units of length per time squared (m/s^2, ft/s^2, etc.).

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