Three Dimensional Geometry Question 370
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 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
Options:
A) Straight line, 60 km
B) Straight line, 30 km
C) Parabola, 60 km
D) Ellipse, 60 km
Show Answer
Answer:
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 $ .
BETA
