Physics-
General
Easy

Question

From the top of a tower of height 50m, a ball is thrown vertically upwards with a certain velocity. It hits the ground 10 s after it is thrown up. How much time does it take to cover a distance A B where A and B are two points 20m and 40m below the edge of the tower? (g equals 10 m s to the power of negative 2 end exponent)

  1. 2.0 s  
  2. 1.0 s  
  3. 0.5 s  
  4. 0.4 s  

The correct answer is: 0.4 s


    Let the body be projected upwards with velocity u from top of tower. Taking vertical downward motion of boy form top of tower to ground, we have
    u equals negative u comma a equals g equals 10 m s to the power of negative 2 end exponent comma s equals 50 m comma t equals 10s
    As s equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent,
    So, 50 equals negative u cross times 10 plus fraction numerator 1 over denominator 2 end fraction cross times 10 cross times 10 to the power of 2 end exponent
    On solving u equals 45 m s to the power of negative 1 end exponent
    If t subscript 1 end subscript and t subscript 2 end subscript are the timings taken by the ball to reach points A and B respectively, then
    20 equals 45 t subscript 1 end subscript plus fraction numerator 1 over denominator 2 end fraction cross times 10 cross times t subscript 1 end subscript superscript 2 end superscript
    and 40 equals negative 45 t subscript 2 end subscript plus fraction numerator 1 over denominator 2 end fraction cross times 10 cross times t subscript 2 end subscript superscript 2 end superscript
    On solving, we get t subscript 1 end subscript equals 9.4 blanks and t subscript 2 end subscript equals 9.8s
    Time taken to cover the distance A B
    equals open parentheses t subscript 2 end subscript minus t subscript 1 end subscript close parentheses equals 9.8 equals 9.4 equals 0.4s.

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