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.
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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