Calculating Position of a Falling Sandbag - Hot Air Balloon Physics Question

[rocomath]

a hot air balloonist, rising vertically with a constant velocity of magnitude 5m/s releases a sandbag at an instant when the balloon is 40m above the ground. after it is released, the sandbag is in free fall.

a) compute position at .250s

i solved it and got ~ 40.9m, which is correct. but why is it +.9m above when it was dropped when the position of the balloonist was 40m? shouldn't it be -.9m?

is it b/c even though the sandbag was dropped at the instant the balloonist was at 40m, the position increased due to the velocity which includes a rise in position within that .250s that they were asking for?

 

[dynamicsolo]

a hot air balloonist, rising vertically with a constant velocity of magnitude 5m/s releases a sandbag at an instant when the balloon is 40m above the ground. after it is released, the sandbag is in free fall.

a) compute position

i solved it and got ~ 40.9m, which is correct. but why is it +.9m above when it was dropped when the position of the balloonist was 40m? shouldn't it be -.9m?

do i have to take into consideration that the balloonist is already moving at an initial velocity of 5m/s and where the sandbag was really dropped, was above 40m?

To one part of your questions, the answer is: yes, you have to take the initial velocity of the sandbag as 5 m/sec upward because it was moving with the balloon just before it was released.

As for part (a), *what* is it you are asked to compute the position of? You should show some of your work, because I am mystified as to what 40.9 meters represents...

 

[m2003]

Yes, that is correct. When the sandbag is released, it will continue to move upwards due to the initial velocity of the balloon, which is why it is +0.9m above the initial position of the balloonist. Additionally, the sandbag will also experience a downward acceleration due to gravity, causing it to fall towards the ground. Therefore, at any given time, the sandbag will have a position that is greater than the initial position of the balloonist.