GATE 2021 MN – Question 57
Fly rock is launched at 45° from the third bench above the pit bottom. Each bench is 8 m wide, 6 m high, with 80° faces, as shown. With g=10 m/s², find minimum launch speed to reach beyond the toe, in m/s to two decimals.
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Correct answer: 9.00 to 11.00
Explanation
The toe is 18 m below launch. Horizontal distance is two 8 m berms plus three face projections: X=16+18cot 80°≈19.1739 m. For 45° launch, y=X−gX²/v². Set y=−18, giving v=√[10X²/(X+18)]≈9.94 m/s. Include face projections as well as berm widths.