Question

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

• A. $60$ km
• B. $30$ km
• C. $45$ km
• D. None of these

Answer 1

The correct option is A $60$ km

Eliminating t from the given equation, we get the equation of the path $\frac{x}{2}=\frac{y}{-4}=\frac{z}{4}=t$

Thus the path of the Rocket represents a straight line passing through the origin for $t=10sec.$

we have $x=20,y=-40,z=40$

Let $\overrightarrow{r}=x\overrightarrow{i}+y\overrightarrow{j}+z\overrightarrow{k}$

$⟹|\overrightarrow{r}|=\sqrt{x^2+y^2+z^2}=\sqrt{400+1600+1600}=60km$