Chapter 9

NCERT
Class 9
Science
Solutions
17. A stone is allowed to fall from the top of a tower 100m high and at the same time another stone is projected vertically when and where the two stones will meet.

Question:

A stone is allowed to fall from the top of a tower 100m high and at the same time another stone is projected vertically when and where the two stones will meet.

Answer:

Case-I

In order to fall, h1 = ut + 0.5 at2

h1 = 0 x t + 0.5 gt2            ...(i)

Case-II,

In order to throw up,

h1 = ut - 0.5 at2

h1 = 25 x t + 0.5 gt2                            …(ii)

from eq(i) and (ii)

h1 + h2 = 25t

100 = 25t

t = 100/25

t = 4s

Therefore the two stones will meet after 4s.

∴ Putting t = 4s in equation (i)

h1 = 0 x 4 + 0.5x 9.8 x 4 x 4         

h1 = 0 + 78.4

h1 = 78.4 m

Therefore both the stone will meet at 78.4m from the top or (100 – 78.4) = 21.6 m from the bottom.

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