a stone is allowed to fall from the top of a tower of 100 m high and at the same time another stone is projected vertically upwards from the ground at a velocity of 25m/s. when and where the two stones would meet
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a stone is allowed to fall from the top of a tower of 100 m high and at the same time another stone is projected vertically upwards from the ground at a velocity of 25m/s. when and where the two stones would meet
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## HERE'S THE SOLUTION -
Height of the tower = 100m
g = 10 m/s 2
velocity of projection of ground projectile = 25 m/s
Velocity of projection of the tower projectile = 0
Let the particles meet at time t and at height h
Thus,
Let "t" = time after which both stones meet
"S" = distance travelled by the stone dropped from the top of tower
(100-S) = distance travelled by the projected stone.
◆ i) For stone dropped from the top of tower
-S = 0 + 1/2 (-10) t²
or, S = 5t²
◆ ii) For stone projected upward
(100 - S) = 25t + 1/2 (-10) t²
= 25t - 5t²
Adding i) and ii) , We get
100 = 25t
or t = 4 s
Therefore, Two stones will meet after 4 s.
◆ ¡¡¡) Put value of t = 4 s in Equation i) , we get
S = 5 × 16
= 80 m.
Thus , both the stone will meet at a distance of 80 m from the top of tower.
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