-->

Atoms And Molecules

Question
CBSEENSC9006116

A boy on a cliff 49 m high drops a stone. One second later he throws a second stone after the first. They both hit the ground at the same time. With what speed did he throw the second stone?

Solution

straight i right parenthesis space For space the space first space stone comma space

straight u space equals space 0 space straight m divided by straight s comma space straight s space equals space minus 49 space straight m comma space straight g space equals space minus 9.8 space straight m divided by straight s squared

Using space the space second space equation space of space motion comma space

space space space space space space space space straight s space equals space ut space plus space 1 half gt squared comma
We space have comma space

minus 49 space equals space 0 space minus space 1 half cross times 9.8 cross times straight t squared
rightwards double arrow space straight t space equals space square root of fraction numerator 49 cross times 2 over denominator 9.8 end fraction end root space equals space square root of 10 space equals space 3.16 space sec

ii right parenthesis thin space Time space taken space by space the space second space stone space to space hit space the space ground comma

straight t space equals space 3.16 space minus space 1 space equals space 2.16 space sec

Now comma space
straight t space equals space 2.16 space straight s comma space straight s space equals space minus 49 space straight m comma space straight g space equals space minus 9.8 space straight m divided by straight s squared

Now space again space using space the space equation comma space

straight i right parenthesis space For space the space first space stone comma space

straight u space equals space 0 space straight m divided by straight s comma space straight s space equals space minus 49 space straight m comma space straight g space equals space minus 9.8 space straight m divided by straight s squared

Using space the space second space equation space of space motion comma space

space space space space space space space space straight s space equals space ut space plus space 1 half gt squared comma
We space have comma space

minus 49 space equals space 0 space minus space 1 half cross times 9.8 cross times straight t squared
rightwards double arrow space straight t space equals space square root of fraction numerator 49 cross times 2 over denominator 9.8 end fraction end root space equals space square root of 10 space equals space 3.16 space sec

ii right parenthesis thin space Time space taken space by space the space second space stone space to space hit space the space ground comma

straight t space equals space 3.16 space minus space 1 space equals space 2.16 space sec

Now comma space
straight t space equals space 2.16 space straight s comma space straight s space equals space minus 49 space straight m comma space straight g space equals space minus 9.8 space straight m divided by straight s squared

Now space again space using space the space equation comma space

straight i right parenthesis space For space the space first space stone comma space

straight u space equals space 0 space straight m divided by straight s comma space straight s space equals space minus 49 space straight m comma space straight g space equals space minus 9.8 space straight m divided by straight s squared

Using space the space second space equation space of space motion comma space

space space space space space space space space straight s space equals space ut space plus space 1 half gt squared comma
We space have comma space

minus 49 space equals space 0 space minus space 1 half cross times 9.8 cross times straight t squared
rightwards double arrow space straight t space equals space square root of fraction numerator 49 cross times 2 over denominator 9.8 end fraction end root space equals space square root of 10 space equals space 3.16 space sec

ii right parenthesis thin space Time space taken space by space the space second space stone space to space hit space the space ground comma

straight t space equals space 3.16 space minus space 1 space equals space 2.16 space sec

Now comma space
straight t space equals space 2.16 space straight s comma space straight s space equals space minus 49 space straight m comma space straight g space equals space minus 9.8 space straight m divided by straight s squared

Now space again space using space the space equation comma space
space space space space space space space space straight s space equals space ut space plus space 1 half gt squared comma
rightwards double arrow space minus 49 space equals space straight u cross times 2.16 space minus space 1 half cross times 9.8 cross times left parenthesis 2.16 right parenthesis squared
rightwards double arrow space minus 49 space equals space 2.16 space straight u space minus space 22.86

rightwards double arrow space space minus 26.14 space equals space 2.16 space straight u

rightwards double arrow space space straight u space equals negative space fraction numerator 26.14 over denominator 2.16 end fraction equals negative 10.1 space straight m divided by straight s