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
(u1cosθ1+u2cosθ2)t=20 ...(i) (u1sinθ1u2sinθ2)t=10 ...(ii)
B
(u1sinθ1+u2sinθ2)t=20 ...(i) (u1sinθ1u2sinθ2)t=10 ...(ii)
C
(u1cosθ1+u2cosθ2)t=20 ...(i) (u1cosθ1u2cosθ2)t=10 ...(ii)
D
(u1sinθ1+u2sinθ2)t=20 ...(i) (u1cosθ1u2cosθ2)t=10 ...(ii)

Solution

## The correct option is A $$\displaystyle \left ( u_{1}\cos \theta _{1}+u_{2}\cos \theta _{2} \right )t= 20$$ ...(i) $$\displaystyle \left ( u_{1}\sin \theta _{1}-u_{2}\sin \theta _{2} \right )t= 10$$ ...(ii)$$\vec { { u }_{ 1 } } ={ u }_{ 1 }cos{ \theta }_{ 1 }\hat { i } +{ u }_{ 1 }sin{ \theta }_{ 1 }\hat { j } \\ \vec { { u }_{ 2 } } =-{ u }_{ 2 }cos{ \theta }_{ 2 }\hat { i } +{ u }_{ 2 }sin{ \theta }_{ 2 }\hat { j } \\ \vec { { u }_{ 1/2 } } =\vec { { u }_{ 1 } } -\vec { { u }_{ 2 } } =({ u }_{ 2 }cos{ \theta }_{ 2 }+{ u }_{ 1 }cos{ \theta }_{ 1 })\hat { i } +({ u }_{ 1 }sin{ \theta }_{ 1 }-{ u }_{ 2 }sin{ \theta }_{ 2 })\hat { j } \\ \vec { { r }_{ 2/1 } } =20\hat { i } +10\hat { j } \\ thus,\\ ({ u }_{ 2 }cos{ \theta }_{ 2 }+{ u }_{ 1 }cos{ \theta }_{ 1 })t=20\quad and\quad ({ u }_{ 1 }sin{ \theta }_{ 1 }-{ u }_{ 2 }sin{ \theta }_{ 2 })t=10$$Physics

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