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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
      Rishabh of Raxaul skated the 10,000 m race in Salt Lake City in 12 min, 58.92 seconds. The oval track is made up of two straight 112.00m sections and two essentially identical semicircular curves. There are two lanes, each 5.00m wide. The 400m Lap starts at \[A\] on the inner straightway, rounds the inner curve, crosses  over in the next straight section in the shortest  diagonal path to the outside lane (the other skater crosses over the other way), and rounds the outer curve, ending up on the adjacent lane at \[B\] (see dotted line). The measurement is made 5cm out from the inner edge of the lane, and is exactly 400m for one lap. What is the radius of the inner curve, R, in m?

    A) \[24.23\]                       

    B) \[25.47\]

    C) \[25.31\]                       

    D) \[25.44\]

    Correct Answer: D

    Solution :

    This is a straight forward problem in calculating the total distance. The only trick is to make sure that in the cross-over lap you use the hypotenuse. The total distance must be precisely 400 m, so we must have \[400=112+\pi \left( R+0.05 \right)+\pi \left( R+5.05 \right)+{{\left( {{112}^{2}}+{{5}^{2}} \right)}^{1/2.}}\] Solving for E given 25.44m.


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