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Question

A stone projected vertically upward moves according to the law S equals 100 t minus 16 t to the power of 2 end exponent. The maximum height reached is

  1. fraction numerator 520 over denominator 3 end fraction units    
  2. fraction numerator 625 over denominator 4 end fraction units    
  3. 653 units    
  4. 560 units    

Hint:

At the point of maximum height velocity of stone becomes 0.

The correct answer is: fraction numerator 625 over denominator 4 end fraction units


    Given : S equals 100 t minus 16 t to the power of 2 end exponent
    We know that V = fraction numerator d s over denominator d t end fraction space
    fraction numerator d s over denominator d t end fraction space equals space 100 fraction numerator d t over denominator d t end fraction v minus space 16 fraction numerator d t squared over denominator d t end fraction space left parenthesis space fraction numerator d x to the power of n over denominator d x end fraction space equals space n x to the power of n minus 1 end exponent right parenthesis
fraction numerator d s over denominator d t end fraction space equals space 100 space minus space 32 t
    At the point of maximum height velocity of stone becomes 0.
    rightwards double arrow space V space equals space fraction numerator d s over denominator d t end fraction space equals space 0
rightwards double arrow 100 space minus space 32 t space equals space 0
rightwards double arrow t space equals space 25 over 8
S u b s t i t u t i n g space t h e space v a l u e space o f space t space i n space S space equals space 100 t space minus space 16 t squared comma space w e space g e t
S space equals space 100 left parenthesis 25 over 8 right parenthesis space minus space 16 space left parenthesis 25 over 8 right parenthesis squared S space equals space 2500 over 8 space minus space 10000 over 64
S space equals space fraction numerator 20000 space minus space 10000 over denominator 64 end fraction
S space equals space 10000 over 64
S space equals space 625 over 4
T h u s comma space t h e space m a x i m u m space h e i g h t space r e a c h e d space i s space 625 over 4 u n i t s

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