Two particles A and B are projected from ground towards each other with speeds 10 m-s and 5-2 m-s at angles 30- and 45- with horizontal from two points separated by a distance of 15 m- Will they collide or not-

X direction : #160;Horizontal range of particle A #160; #160; #160; #160; R_A #160;=V_A^2 sin (60)g #160;= 10^2 × 0.8669.8 #160;= 8.84 ...

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Byju's Answer

Standard XII

Physics

Summary for Maximum Range and the Dominating Component

Two particles...

Question

Two particles $A$ and $B$ are projected from ground towards each other with speeds $10 m / s$ and $5 \sqrt{2} m / s$ at angles $30^{\circ}$ and $45^{\circ}$ with horizontal from two points separated by a distance of $15 m$ . Will they collide or not?

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Solution

x direction :
Horizontal range of particle A $R_{A} = \frac{V_{A}^{2} s i n (60)}{g} = \frac{10^{2} \times 0.866}{9.8} = 8.84$ m
Horizontal range of particle B $R_{B} = \frac{V_{B}^{2} s i n (90)}{g} = \frac{(5 \sqrt{2})^{2} \times 1}{9.8} = 5.1$ m
$∴$ Maximum horizontal distance covered by both particles $= 5.1 + 8.84 = 13.94 < 15$ m
Thus the particle will not collide in mid air.

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Two particles A and B are projected from ground towards each other with speeds 10 m/s and 5√2 m/s at angles 30∘ and 45∘ with horizontal from two points separated by a distance of 15 m. Will they collide or not?

x direction : Horizontal range of particle A RA=V2Asin(60)g=102×0.8669.8=8.84 mHorizontal range of particle B RB=V2Bsin(90)g=(5√2)2×19.8=5.1 m∴ Maximum horizontal distance covered by both particles =5.1+8.84=13.94<15 mThus the particle will not collide in mid air.

Two particles $A$ and $B$ are projected from ground towards each other with speeds $10 m / s$ and $5 \sqrt{2} m / s$ at angles $30^{\circ}$ and $45^{\circ}$ with horizontal from two points separated by a distance of $15 m$ . Will they collide or not?