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Atoms And Molecules

Question
CBSEENSC9006120

A man is standing at the top of a 60 m high tower. He throws a ball vertically upwards with a velocity of 20 m/s. After what time will the ball pass him going downward ? How long after its release will the ball reach the ground ? (Take g = 10 m/s2)

Solution

(i) When the ball passes the man, net displacement = 0
That is, s = 0 m
                      
Also comma space

straight u space equals space plus 20 space straight m divided by straight s comma space straight g space equals space minus 10 space straight m divided by straight s squared

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

straight s space equals space ut space plus space 1 half at squared
0 space equals space 20 space cross times space straight t space plus space 1 half space cross times space left parenthesis negative 10 right parenthesis space straight t squared
straight i. straight e. comma space space straight t space equals space 20 divided by 5 space equals space 4 space sec. space

ii right parenthesis space Now comma space distance space travelled space by space the space ball comma space straight s space equals space minus 60 space straight m

Negative space sign space implies space it space is space straight a space downward space displacement. space

Using space second space equation space of space motion comma space

space space space space space space space straight s space equals space ut space plus space 1 half at squared
therefore space minus 60 space equals space 20 cross times straight t space minus space 1 half cross times 10 cross times straight t squared space
rightwards double arrow space minus 12 space equals space 4 straight t space minus space straight t squared

rightwards double arrow space straight t squared space minus space 4 straight t space minus space 12 space equals space 0 space

rightwards double arrow left parenthesis straight t minus 6 right parenthesis space left parenthesis straight t plus 2 right parenthesis space equals space 0

straight i. straight e. comma space straight t space equals space 6 space or space straight t space equals negative 2 space

Since comma space time space cannot space be space negative space
straight t space equals space 6 space sec