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 ?`

Explanation

Eliminating `t` from the given equations, we get equation of the path.
`" "(x)/(2)=(y)/(-4)=(z)/(4)`
or `" "(x)/(1)=(y)/(-2)=(z)/(2)`
Thus, the path of the rocket represents a straight line passing through the origin.
For `" "t=10` s, we have
`" "x=20, y=-40 and z=40`
and `" "|vecr|=|vec(OM)|=sqrt(x^(2)+y^(2)+z^(2))`
`" "sqrt(400+1600+1600) = 60 ` km