The equations of motion of a rocket are: x = | vedclass

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(A) Eliminating $t$ from the given equations,we get the equation of the path:$\frac{x}{2} = \frac{y}{-4} = \frac{z}{4}$ or $\frac{x}{1} = \frac{y}{-2}

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Straight line,$60 	ext{ km}$

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(A) Eliminating $t$ from the given equations,we get the equation of the path:$\frac{x}{2} = \frac{y}{-4} = \frac{z}{4}$ or $\frac{x}{1} = \frac{y}{-2} = \frac{z}{2}$.This represents a straight line passing through the origin.For $t = 10 	ext{ s}$,the coordinates are:$x = 2(10) = 20 	ext{ km}$,$y = -4(10) = -40 	ext{ km}$,$z = 4(10) = 40 	ext{ km}$.The distance from the origin $O(0, 0, 0)$ is given by:$d = \sqrt{x^2 + y^2 + z^2} = \sqrt{20^2 + (-40)^2 + 40^2}$$d = \sqrt{400 + 1600 + 1600} = \sqrt{3600} = 60 	ext{ km}$.

The equations of motion of a rocket are: $x = 2t, y = -4t, z = 4t$ where the time $t$ is given in seconds,and the coordinates of a moving point in kilometers. What is the path of the rocket? At what distance will the rocket be from the starting point $O(0, 0, 0)$ in $10$ seconds?

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