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Atoms And Molecules

Question
CBSEENSC9006117

A ball is dropped from the jumping board of a swimming pool, which is at a height of 20 m. A second ball is thrown from the same board after one second with initial velocity u. Both the balls hit the water together. What was the initial velocity with which the second ball was thrown ? Do they hit water with the same velocity ? Explain your answer.

Solution

(i) Given that, 
s = -20 m, u = 0 m/s and g = -10 m/s2
Now, according to the third equation of motion, 
straight v squared space equals space straight u squared space plus space 2 gs
space space space space equals space 0 plus 2 cross times left parenthesis negative 10 right parenthesis cross times left parenthesis negative 20 right parenthesis space equals space 400
straight i. straight e. comma space straight v space equals space square root of 400 space equals space 20 space straight m divided by straight s

Downward space velocity space is space taken space as space negative. space

Therefore comma space

straight v space equals space minus space 20 space straight m divided by straight s 
ii) Now, 
Distance travelled by the ball, s = -40 m
u = 0 and g = -10 m/s2 
Now, using the third equation of motion, 
straight v squared space equals space straight u squared space plus space 2 gs

space space space space equals space 0 plus 2 cross times left parenthesis negative 10 right parenthesis cross times left parenthesis negative 40 right parenthesis space equals space 800

straight i. straight e. comma space straight v space equals space square root of 800

space space space space space space space space space space space equals space plus-or-minus space square root of 800

space space space space space space space space space space space equals space minus 20 square root of 2 space straight m divided by straight s

Because space the space velocity space is space acting space in space the space downward space direction.