A hot air balloon is rising straight upward with a constant speed of 8.80 m/s. When the basket of the balloon is 100.0 m about the ground a bag of sand tied to the basket comes loose. What is the greatest height of the bag of sand during its fall to the ground?

Expert Answers

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  • When the balloon goes upward with a velocity of 8.8m/s all items inside it has the same velocity of 8.8m/s.
  • When the sand bag get loosed it also have that speed at the moment of loose.
  • The balloon goes upwards because it has a force upward because of hot air.
  • So all the parts inside the balloon is subjected to this force.
  • When the sand bag get loosened it will loss the connection with the balloon.
  • So this force due to hot air will no longer apply on sand bag.
  • Due to the sand bag's weight it should come down.
  • Since it has a velocity of 8.8m/s at the moment of loose it will go some distance upward under gravity and then start to come down.

Using equation of motion;

`uarrv^2 = u^2+2as`

`v = 0` since at the greatest height it suddenly get to rest.

`u = 8.8m/s`

`g = -9.8m/s^2` Since the bag travels under gravity

`s = ?`

`uarrv^2 = u^2+2as`

`0 = 8.8^2-2xx9.81xxs`

`s = 3.95m`

So the height from ground is `100+3.95 = 103.95m.`

Assumption

There is no air resistance applied on the sand bag.

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