A particle is fired from \( A \) in the diagonal plane of a building of dimension \( 20 \mathrm{...

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A particle is fired from \( A \) in the diagonal plane of a building of dimension \( 20 \mathrm{~m} \) (length) \( \times 15 \mathrm{~m} \) (breadth) \( \times 12.5 \) (height) just clears the roof diagonally and falls on the other side of the building at \( B \). It is observed that the particle is travelling at an angle \( 45^{\circ} \) with the horizontal when it clears the edges \( P \) and \( Q \) of the diagonal. Take \( g=10 \mathrm{~m} / \mathrm{s}^{2} \).
The speed of the particle at point \( P \) will be:
(1) \( 5 \sqrt{10} \mathrm{~m} / \mathrm{s} \)
(2) \( 10 \sqrt{5} \mathrm{~m} / \mathrm{s} \)
(3) \( 5 \sqrt{15} \mathrm{~m} / \mathrm{s} \)
(4) \( 5 \sqrt{5} \mathrm{~m} / \mathrm{s} \)
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