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Motion In Straight Line

Question
CBSEENPH11020683

A ball is dropped from  a high-rise platform at t=0 starting from rest. After 6s another ball is thrown downwards from the same platform with a speed v. The two balls meet at t= 18s. What is the value of v? (take g= 10 ms-2)

  • 74 ms-2

  • 55 ms-1

  • 40 ms-1

  • 60 ms-1

Solution

A.

74 ms-2

For space first space ball space comma space straight u space equals space 0
therefore comma
straight s subscript 1 space equals space 1 half space gt subscript 1 superscript 2 space equals space 1 half space straight x space straight g space left parenthesis 18 right parenthesis squared
For space second space ball comma space initial space velocity space equals space straight v
therefore comma space
straight s subscript 2 space equals space vt subscript 2 space plus space 1 half space gt squared
straight t subscript 2 space equals space 18 minus 6 space equals space 12 space straight s
straight s subscript 2 space equals space straight v space straight x space 12 space plus space 1 half straight g space left parenthesis 12 right parenthesis squared
Here comma space space straight s subscript 1 space equals space straight s subscript 2
1 half straight g left parenthesis 18 right parenthesis squared space equals space 12 space straight v space plus space 1 half space left parenthesis straight g right parenthesis space left parenthesis 12 right parenthesis squared
straight v equals space 74 space ms to the power of negative 1 end exponent