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Q.

A particle is projected with a speed u at an angle θ with horizontal from point A. It strikes elastically with a vertical wall at height h/2. It rebounds and reaches maximum height h and falls back on the ground at point B as shown in figure. Distances from A to wall and from wall to B are x1 and x2, respectively, and time to cover x1 and x2 are t1 and t2 respectively. Match the values in column I with the expression in column II.

Question Image
 Column I Column II
i2px2x1x2+x1orx2+x1x2x1
ii12qt2t1t2+t1ort2+t1t2t1
iii1rusinθg(t1+t2)
iv12sucosθ(t1+t2)(x1+x2)

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a

(i) r, s; (ii) p; (iii) s; (iv) q

b

(i) p, q; (ii) s; (iii) s ; (iv) r, s 

c

(i) p; (ii) r; (iii) s; (iv) q

d

(i) p, q; (ii) p, q; (iii) s; (iv)  r

answer is A.

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Detailed Solution

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x1=ucosθt1;x2=ucosθt2

2hg=T2=t1+t22;2h2g=t2t12

Dividing, t1+t2t1t2=2 Also, x2x1x2+x1=t2t1t2+t1

T=2usinθg;t1+t2=2usinθg

12=usinθg(t1+t2)

Also x1+x2=ucosθ(t1+t2), ucosθ(t1+t2)x1+x2=1

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