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Atoms And Molecules

Question
CBSEENSC9006115

A helicopter is ascending with a velocity of 2 m/s at a height of 24 m when it drops a mail packet. The packet contains material, which can be damaged if it hits ground with velocity of magnitude greater than 72 km / h. Was the packet damaged? Explain your answer.
(Take g = 10 m/s2)

Solution

Velocity space of space the space helicopter comma space straight u space equals space 2 space straight m divided by straight s

Height space of space the space helicopter space when
the space mail space packet space is space dropped comma space straight h space equals space 24 space straight m

Now comma space using space the space equation space of space motion comma

space space space space space space space straight v squared space equals space straight u squared plus 2 g s
space
space space space space space space space space space space space space equals space 2 squared plus 2 space cross times space left parenthesis negative 24 right parenthesis space cross times space left parenthesis negative 10 right parenthesis

space space space space space space space space space space space space equals 4 space plus 480 space equals space 484

rightwards double arrow space space space space space straight v space equals space plus-or-minus square root of 484

i. e. comma space straight v space equals space minus 22 space straight m divided by straight s space space space space space space space space space left parenthesis Downward space velocity space is space taken space minus straight v e right parenthesis

Safe space velocit y space equals space 72 space k m divided by straight h space equals fraction numerator 72 space cross times 1000 over denominator 3600 end fraction space equals 20 space straight m divided by straight s

The packet reaches the ground with a velocity (22 m/s), which is greater than the safe velocity of 20 m/s. So the packet is damaged.