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Distance

Two particles...

Question

Two particles A and B are projected from the ground towards each other with speeds 10m/s and 5√2 m/s at angles 30° and 45° respectively with horizontal from two points separated by a distance of 15m . Will the collide?

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Solution

If the particles collide they must be at the same point at the same time. So their time of flight should be equal. Let's check,
$T subscript 1 equals fraction numerator 2 u subscript 1 sin space theta subscript 1 over denominator g end fraction T subscript 1 equals fraction numerator 2 cross times 10 cross times sin space 30 over denominator 10 end fraction equals 2 cross times 1 half equals 1 space s e c T subscript 2 equals fraction numerator 2 cross times 5 square root of 2 space sin space 45 over denominator 10 end fraction equals fraction numerator 10 square root of 2 cross times begin display style fraction numerator 1 over denominator square root of 2 end fraction end style over denominator 10 end fraction equals 1 T subscript 1 equals T subscript 2 S o space t h e y space w i l l space c o l l i d e$

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