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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Critical Thinking

  • question_answer
    The equation of motion of a rocket are: \[x=2t,\,y=-4t,\] \[\,z=4t\] where the time 't' is given in seconds, and the co-ordinates of a moving point in kilometers. What is the path of the rocket. At what distance will be the rocket be from the starting point 0(0, 0, 0) in 10 seconds

    A) Straight line, 60 km

    B) Straight line, 30 km

    C) Parabola, 60 km

    D) Ellipse, 60 km

    Correct Answer: A

    Solution :

    • Eliminating 't' from the given equations, we get the equatin of the path, \[\frac{x}{2}=\frac{y}{-4}=\frac{z}{4}\] or \[\frac{x}{1}=\frac{y}{-2}=\frac{z}{2}\]     
    • Thus, the path of the rocket represents a straight line passing through the origin.           
    • For \[t=10\] sec. we have, \[x=20,\,y=-40,\,z=40\]           
    • and \[|\vec{r}|\,=\,|\overrightarrow{OM}|\,=\sqrt{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}}\]                        
    • \[=\sqrt{400+1600+1600}=60km\].                   


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