NEET Sample Paper NEET Sample Test Paper-14

  • question_answer 29) At time t = 0. A bullet is fired vertically upwards with-a speed of\[98\text{ }m{{s}^{-1}}.\] A second bullet is fired vertically upwards with the same speed at \[t=5\]s. Then:

    A)  the two bullets will be at the same height above the ground at t = 12.5 s.                  

    B)  the two bullets will reach back their stating  point at t = 25 s.                           

    C)  the two bullets will have the same speed at  t = 20 s.                                 

    D)  the maximum height attained by either bullet will be 980 m.                           

    Correct Answer: A

    Solution :

    The two bullets will be at the same height at \[t=n\]if \[98-4.9\,{{n}^{2}}=98(n-5)-4.9\,{{(n-5)}^{2}}.\] This gives\[~n=12.5\text{ }s.\]The time to reach the highest point is given by 0 = 98 - 9.8 t, i.e., t = 10 sec. Therefore, the time of flight is \[2\times 10\,s\] or 20 sec. The speed of the first bullet at t = 20 sec. is 98 m/s again while that of the second bullet is \[(98-9.8\times 0.5)\,m/s\]or 49 m/s. The maximum heights attained are 490 m each. Hence, the correction option is [a].

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