The equations of motion of a rocket are: x = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Eliminating $t$ from the given equations,we get the equation of the path:$\frac{x}{2} = \frac{y}{-4} = \frac{z}{4}$ or $\frac{x}{1} = \frac{y}{-2}

Vedclass · Accepted Answer

Straight line,$60 	ext{ km}$

Vedclass · Answer

(A) Eliminating $t$ from the given equations,we get the equation of the path:$\frac{x}{2} = \frac{y}{-4} = \frac{z}{4}$ or $\frac{x}{1} = \frac{y}{-2} = \frac{z}{2}$.This represents a straight line passing through the origin.For $t = 10 	ext{ s}$,the coordinates are:$x = 2(10) = 20 	ext{ km}$,$y = -4(10) = -40 	ext{ km}$,$z = 4(10) = 40 	ext{ km}$.The distance from the origin $O(0, 0, 0)$ is given by:$d = \sqrt{x^2 + y^2 + z^2} = \sqrt{20^2 + (-40)^2 + 40^2}$$d = \sqrt{400 + 1600 + 1600} = \sqrt{3600} = 60 	ext{ km}$.

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

Similar Questions

If the lines $2x = ky = -z$ and $6x = -y = -4z$ are perpendicular to each other, then the value of $k$ is:

The acute angle between the line joining the points $(2,1,-3)$ and $(-3,1,7)$ and a line parallel to $\frac{x-1}{3}=\frac{y}{4}=\frac{z+3}{5}$ is

The angle between the two lines $\frac{x-2}{2} = \frac{2-y}{3} = \frac{z-1}{2}$ and $\frac{x-1}{2} = \frac{y+1}{1} = \frac{z-3}{-3}$ is . . . . . . .

If $p$ is the shortest distance between the lines $\frac{x + 1}{7} = \frac{y + 1}{-6} = \frac{z + 1}{1}$ and $\vec{r} = (3\hat{i} + 5\hat{j} + 7\hat{k}) + \mu(\hat{i} - 2\hat{j} + \hat{k})$, then $[p]$ is... (where $[.]$ denotes the greatest integer function.)

If the line passing through $(5, 1, a)$ and $(3, b, 1)$ intersects the $yz$-plane at $\left(0, \frac{17}{2}, \frac{-13}{2}\right)$,then find the values of $a$ and $b$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module