A fountain jet situated at a height of 11.25m above the ground projects water droplets in all directions with velocity of $20 ms^{- 1}$ . Calculate the maximum distance (in m)on ground reached by any water droplet.

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− 11.25 = x tan θ − 2 1 ​ 2 0 2 10 x 2 ​ ( 1 + tan 2 θ ) − 11.25 − 80 x 2 ​ tan 2 θ + x tan θ − 80 x 2 ​ + 11.25 b 2 − 4 a c x 2 − 4 ( − 80 x 2 ​ ) ( − 80 x 2 ​ + 11.25 ) 1 + 20 1 ​ ( 11.25 − 80 x 2 ​ ) 20 31.25 ​ x 2 x 2 x ​ = x tan θ − 80 x 2 ​ − 80 x 2 ​ tan 2 θ = 0 ≥ 0 ≥ 0 ≥ 0 ≥ 1600 x 2 ​ ≤ 31.25 × 80 ≤ 2500 ≤ 50 m ​

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