The equation of motion of a missile is x = 3t, y = -4t, z = t where time 't' is in seconds and the distance is measured in kilometres.
At what distance will the rocket be from the point (0, 0, 0) in 5 seconds?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\sqrt{650}$ kms
let coordinates after 5 sec be
$P(x, y, z)$
at $t=5$
$x=3×5=15$
$y=-4×5=-20$
$z=5$
so $P(15,-20,5)$
so $O(0,0,0)$
$OP=\sqrt{15^2+20^2+5^2}$
$=\sqrt{225+400+25}$
$=\sqrt{650}$ kms