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Motion in A Straight Line question

2024 · 27 Jan · Shift 2 · Q85
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  5. /2024 · 27 Jan · Shift 2 · Q85

Motion in A Straight Line question

2024 · 27 Jan · Shift 2 · Q85

JEE MainPhysicsMotion in A Straight LineNumerical+4 / −1
A body falling under gravity covers two points AAA and BBB separated by 80 m80 \mathrm{~m}80 m in 2 s2 \mathrm{~s}2 s. The distance of upper point A from the starting point is ‾m\underline{\hspace{2cm}}\mathrm{m}​m(use g=10 ms−2\mathrm{g}=10 \mathrm{~ms}^{-2}g=10 ms−2).
Numerical answer
View written solutionFree

Correct answer: 45

  1. Let the body start from rest and fall vertically downward.
    Suppose the upper point AAA is at a distance xxx from the starting point.

  2. Velocity at point AAA
    Using vA2=2gxv_A^2 = 2gxvA2​=2gx with g=10 m s−2g=10\,\text{m s}^{-2}g=10m s−2, vA2=20xv_A^2 = 20xvA2​=20x so vA=20xv_A = \sqrt{20x}vA​=20x​

  3. Motion from AAA to BBB
    The body travels from AAA to BBB in t=2 st=2\,\text{s}t=2s, covering distance s=80 ms=80\,\text{m}s=80m under acceleration g=10 m s−2g=10\,\text{m s}^{-2}g=10m s−2.

    Using s=vAt+12gt2s = v_A t + \frac{1}{2}gt^2s=vA​t+21​gt2 80=vA(2)+12(10)(22)80 = v_A(2) + \frac{1}{2}(10)(2^2)80=vA​(2)+21​(10)(22) 80=2vA+2080 = 2v_A + 2080=2vA​+20 2vA=602v_A = 602vA​=60 vA=30 m s−1v_A = 30\,\text{m s}^{-1}vA​=30m s−1

  4. Now find xxx
    From vA2=20xv_A^2 = 20xvA2​=20x 302=20x30^2 = 20x302=20x 900=20x900 = 20x900=20x x=45 mx = 45\,\text{m}x=45m

  5. Final Answer
    The distance of point AAA from the starting point is 45 m\boxed{45\,\text{m}}45m​

  6. Comparison with stored answer
    Stored correct answer = 454545
    Derived answer = 454545
    Hence, they agree.

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