Two particles \( \mathrm{A} \) and \( \mathrm{B} \) are projected simultaneously from the two to...

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Two particles \( \mathrm{A} \) and \( \mathrm{B} \) are projected simultaneously from the two towers of height \( 10 \mathrm{~m} \) and \( 20 \mathrm{~m} \)
P
W respectively. Particle \( A \) is projected with an initial speed of \( 10 \sqrt{2} \mathrm{~m} / \mathrm{s} \) at an angle of \( 45^{\circ} \) with horizontal, while particle \( B \) is projected horizontally with speed \( 10 \mathrm{~m} / \mathrm{s} \). If they collide in air, what is the distance \( \mathrm{d} \) between the towers?
(1) \( 10 \mathrm{~m} \)
(2) \( 20 \mathrm{~m} \)
(3) \( 30 \mathrm{~m} \)
(4) \( 40 \mathrm{~m} \)
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