Calculating Time for an Object to Fall in One Dimension

[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?

Thanks for taking your time to read.

 

[Kalvarin]

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 :)

 

[kuruman]

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 ...

 

[rl.bhat]

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

 

[ShamTheCandle]

Thanks all! I appreciate your help.