Class 9 Science - Chapter Gravitation NCERT Solutions | A stone is allowed to fall from the top

Welcome to the NCERT Solutions for Class 9th Science - Chapter Gravitation. This page offers a step-by-step solution to the specific question from Excercise ".$ex_no." , Question 17: a stone is allowed to fall from the top of a tower....
Question 17

A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.

Answer

Let the two stones meet after a time t.

(i) For the stone dropped from the tower:

Initial velocity, u = 0 m/s

Let the displacement = s

Acceleration due to gravity, g = 9.8 m s−2

From the equation of motion,

                  ...(1)

(ii) For the stone thrown upwards:

Initial velocity, u = 25 m/s

Let the displacement = s'.

Acceleration due to gravity, g = −9.8 m s−2

Equation of motion,

              ...(2)

The combined displacement is ;

In 4 s, the falling stone has covered a distance given by equation (1) as

Therefore, the stones will meet after 4 s and the distance is 80 m from the top.

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