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Summary for Time, Height and Range

Two particles...

Question

Two particles A and B are projected simultaneously in a vertical plane as shown in figure. They collide at time t in air. Write down two necessary equations for collision to take place.

A

(u_{1} cos θ_{1} + u_{2} cos θ_{2}) t = 20

...(i)

(u_{1} sin θ_{1} - u_{2} sin θ_{2}) t = 10

...(ii)

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B

(u_{1} sin θ_{1} + u_{2} sin θ_{2}) t = 20

...(i)

(u_{1} sin θ_{1} - u_{2} sin θ_{2}) t = 10

...(ii)

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C

(u_{1} cos θ_{1} + u_{2} cos θ_{2}) t = 20

...(i)

(u_{1} cos θ_{1} - u_{2} cos θ_{2}) t = 10

...(ii)

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D

(u_{1} sin θ_{1} + u_{2} sin θ_{2}) t = 20

...(i)

(u_{1} cos θ_{1} - u_{2} cos θ_{2}) t = 10

...(ii)

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Solution

The correct option is A $(u_{1} cos θ_{1} + u_{2} cos θ_{2}) t = 20$ ...(i) $(u_{1} sin θ_{1} - u_{2} sin θ_{2}) t = 10$ ...(ii)
$_{1} = u_{1} c o s θ_{1}^i + u_{1} s i n θ_{1}^j_{2} = - u_{2} c o s θ_{2}^i + u_{2} s i n θ_{2}^j_{1 / 2} =_{1} -_{2} = (u_{2} c o s θ_{2} + u_{1} c o s θ_{1})^i + (u_{1} s i n θ_{1} - u_{2} s i n θ_{2})^j_{2 / 1} = 20^i + 10^j t h u s, (u_{2} c o s θ_{2} + u_{1} c o s θ_{1}) t = 20 a n d (u_{1} s i n θ_{1} - u_{2} s i n θ_{2}) t = 10$

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