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Grade 11Mechanics

two balls of equal masses are thrown upwards , along the same vertical direction at an interval of 2 seconds , with the same initial velocity of 40m/s. Then these will collide at a height of (Take g=10m/s2)
  1. 120m
  2. 75m
  3. 200m
  4. 45m

Profile image of Dishari Das
7 Years agoGrade 11
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1 Answer

Profile image of Arun
7 Years ago
Displacement of 1st mass = s1 = 40 t - 1/2 * 10 * t²  =  5 (8 t - t²)
Displacement of 2nd mass = s2 = 40 (t-2) - 1/2 * 10 * (t-2)²
                     = 5 [ 8(t-2) - (t-2)² ] = 5 [ 8 t - 16 - t² + 4 t - 4 ]
                   = 5 [ 8 t - t² +4 t - 20 ]
s1 = s2    =>       4 t - 20 =0                 =>  t = 5 sec
s1 = height at which they collide = 5( 8*5 - 5²) = 5 * 15 = 75 meters