Q34 / 72 · NTA Abhyas (JEE Main) 2020 · Physics · Motion In Two Dimensions

Taking X-axis along horizontal and Y-axis along vertical, with what minimum speed must a particle be projected from the origin so that it is able to pass through a given point (30 m, 40 m)? Take g = 10 m s-2

  • A
    60 m s-1
  • Correct answer
    B
    30 m s-1
  • C
    50 m s-1
  • D
    40 m s-1

Solution

Using equation of trajectory for a projectile motion :

y=xtan⁡θ-gx22u21+tan2⁡θ

For the projectile to pass through (30 m, 40 m) :

40 = 30 tan α - g (30) 2 2u 2 1 + tan 2 α

or      900 tan2 α - (6u2 tan α) + (900 + 8u2) = 0

For real value of α. The discriminant of a quadratic equation b2-4ac≥0

                     (6u2)2 ≥ 3600 (900 + 8u2)

or        (u4 - 800 u2) ≥ 9,00,00

or           (u2 - 400)2 ≥ (2,50,000)

or               u2 - 400 ≥ 500

or             u2 ≥ 900  or  u ≥ 30 m s-1

Hence, the correct answer is option: 'B'.

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