A bag of ballast is accidentally dropped from a balloon which is stationary at an altitude of 4900m. How long does it take for the bag to hit the ground?

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Answer 1 · 2018-03-05T04:25:04

#31.6# s

A good equation to know for calculating time of falls due to gravity alone is:

#h = 1/2 g t^2 -> t = sqrt((2h)/g)#

Here, we can use #h = 4900# m. There is no gravity mentioned, so I will simply use #9.8# m/#s^2#.

#t = sqrt(((2)(4900))/9.8) =31.6# s

Answer 2 · 2018-03-05T04:45:50

Use the equations of motion to answer the question.

It is given that balloon is stationary at height #(s) = "4900 m"#. The initial velocity #(u) = "0 m/s"#.

As it falls in the downward direction, it accelerates with an acceleration of #g = "9.81m/s"^2# (for simple calculations, #g = "9.8 m/s"^2#)

So

#4900 = 0*t + 1/2*g*t^2#

On solving

#t = sqrt((2 * 4900)/9.8)#

#t = sqrt(1000) " s"#