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The equations of motion of a rocket a...

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

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AI Generated Solution

To solve the problem step by step, we will first derive the path of the rocket by eliminating the parameter \( t \) from the equations of motion, and then we will calculate the distance from the starting point \( O(0,0,0) \) after \( 10 \) seconds. ### Step 1: Write down the equations of motion The equations of motion of the rocket are given as: \[ x = 2t, \quad y = -4t, \quad z = 4t \] ...
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