A fire nozzle situated at a distance 20 m from the building discharges water with an initial velocity of $20 ms^{- 1}$ as shown in figure. If the height of the building is 18 meter (above nozzle), find the minimum possible height x (in m) of that portion of the building that escapes the water jets.

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Applying the equation of trajectory: y = 20 tan α − 2 1 ​ u 2 g ( 20 ) 2 ​ ( 1 + tan 2 α ) y = 20 tan α − u 2 2000 ​ − u 2 2000 ​ tan 2 α ( u 2 2000 ​ ) tan 2 α − ( 20 ) tan α + ( y + u 2 2000 ​ ) = 0 For real values of tan α : b 2 − 4 a c ≥ 0 ∴ 400 ≥ 4 ( 20 × 20 2000 ​ ) ( y + 20 × 20 2000 ​ ) 100 ≥ 5 ( y + 5 ) 20 ≥ y + 5 15 ≥ y ∴ y ma x ​ = 15 So, x = 18 − 15 = 3 m .

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