Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is 3 and the maximum height reached by it is 102 m. Then the maximum height reached by the other in metre is -
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We know that if two stones have same horizontal range, then this implies that both are projected at θ and 90°−θ.
Here,
θ= π/3 = 60°=
∴90°−θ=90°−60°=30°
For first stone,
Maximum height = 102 = u² sin²60°/2g
For second stone,
Maximum height,
h = u²sin²30°/2g
∴h1/h2 = sin²60°/sin²30°
h1/h2 = 3/4 × 4/1
h1 = 3 h2
So, 102 = 3× h2
102/3 = h2
h2 = 34 m
Here,
θ= π/3 = 60°=
∴90°−θ=90°−60°=30°
For first stone,
Maximum height = 102 = u² sin²60°/2g
For second stone,
Maximum height,
h = u²sin²30°/2g
∴h1/h2 = sin²60°/sin²30°
h1/h2 = 3/4 × 4/1
h1 = 3 h2
So, 102 = 3× h2
102/3 = h2
h2 = 34 m
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