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Standard XII

Physics

Frames of Reference

An elevator w...

Question

An elevator without a ceiling is ascending up with an acceleration of $5 {ms}^{- 2}$ . A boy on the elevator shoots a ball in vertical upward direction from a height of $2 m$ above the floor of elevator. At this instant the elevator is moving up with a velocity of $10 {ms}^{- 1}$ , and the floor of the elevator is at a height of $50 m$ from the ground. The initial speed of the ball is $15 {ms}^{- 1}$ with respect to the elevator. Consider the duration for which the ball strikes the floor of elevator in answering following questions. ( $g = 10 {ms}^{- 2}$ )

2.13 s

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2.0 s

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1.0 s

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3.12 s

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Solution

The correct option is A $2.13 s$
Given: ${\to u}_{L G} = + 10^j, {\to a}_{L G} = S^j {\to u}_{B L} = 15^j, {\to a}_{B G} = - 10^j S_{B L} = u_{B L} t + \frac{1}{2} a_{B L} t^{2} \Rightarrow - 2 = [15] t + \frac{1}{2} [- 10 - 5] t^{2} \Rightarrow - 4 = 30 t - 15 t^{2} \Rightarrow 15 t^{2} - 30 t - 4 = 0 t = \frac{- (- 30) \pm \sqrt{900 + 4 (60)}}{2 (15)} t \approx 2.13 s$

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The correct option is A 2.13 sGiven: →uLG=+10^j, →aLG=S^j→uBL=15^j, →aBG=−10^jSBL=uBLt+12aBLt2⇒−2=[15]t+12[−10−5]t2⇒−4=30t−15t2⇒15t2−30t−4=0t=−(−30)±√900+4(60)2(15)t≈2.13 s