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NEET2019PhysicsMotion in Two DimensionsActual

Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 ~m apart and of same height of 200 ~m with the same velocity of 25 ~m / s . When and where will the two bullets collides. ( g =10 ~m / s ^2 )

Options

  1. AAfter 2 ~s at a height 180 ~m
  2. BAfter 2 ~s at a height of 20 ~m
  3. CAfter 4 ~s at a height of 120 ~m
  4. DThey will not collide

Correct answer

A. After 2 ~s at a height 180 ~m

Step-by-step solution

Given, distance between the two buildings d =100 ~m height of each tower, h =200 ~m speed of each bullet, v =25 ~ms ⁻¹ The situation can be shown as below where, x be the vertical distance travelled from the top of the building and t be the time at which they collide. As two bullets are fired toward each other, So, their relative velocity will be v _ rel =25-(-25)=50 ~ms ⁻¹ Then, time t = d v _ rel = 100 50 =2 ~s The distance or height at which they collide is calculated from equation of motion, x = ut + 1 2 at ^2

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