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Motion in A Plane question

2023 · 24 Jan · Shift 1 · Q58
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  5. /2023 · 24 Jan · Shift 1 · Q58

Motion in A Plane question

2023 · 24 Jan · Shift 1 · Q58

JEE MainPhysicsMotion in A PlaneMCQ+4 / −1
The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :
  1. A
    136 m
  2. B
    272 m
  3. C
    68 m
  4. D
    192 m
View written solutionFree

Correct answer: B

  1. Let the maximum speed with which the man can throw the ball be uuu.

  2. Maximum vertical height is obtained when he throws the ball vertically upward.

    Using H=u22gH = \frac{u^2}{2g}H=2gu2​ given H=136 mH = 136\,\text{m}H=136m.

    So, u22g=136\frac{u^2}{2g} = 1362gu2​=136 u2=272gu^2 = 272gu2=272g

  3. Maximum horizontal distance is the maximum range on level ground, which occurs at angle 45∘45^\circ45∘.

    Range formula: Rmax⁡=u2gR_{\max} = \frac{u^2}{g}Rmax​=gu2​

    Substituting u2=272gu^2 = 272gu2=272g, Rmax⁡=272gg=272 mR_{\max} = \frac{272g}{g} = 272\,\text{m}Rmax​=g272g​=272m

  4. Therefore, the maximum horizontal distance is 272 m\boxed{272\,\text{m}}272m​

  5. Option check:

    • A: 136 m136\,\text{m}136m ✗
    • B: 272 m272\,\text{m}272m ✓
    • C: 68 m68\,\text{m}68m ✗
    • D: 192 m192\,\text{m}192m ✗

Hence, the correct option is B.

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