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 kilomete

Question

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 kilomete

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 ?`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Related Questions

The coordinates of the centre of the circle having the points (9, 3) and (1, -1) as the end points of the diameter is ………………..

2 Answers 4 Views

The speed(v) of a particle moving along a straight line is given by `v=(t^(2)+3t-4` where v is in m/s and t in seconds. Find time t at which the parti

2 Answers 6 Views

The coordinates of a moving particle at time t are given by `x=ct^(2)` and `y=bt^(2)`. The speed of the particle is given by :-

2 Answers 4 Views

Convert the following points from polar coordinates to the corresponding Cartesian coordinates. (i) `(2,pi//3)` (ii) `(0.pi//2)` (iii) `(-sqrt(2),pi//

2 Answers 5 Views

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) `(2,pi)` (ii) `(sqrt(3),pi//6)`

2 Answers 5 Views

Convert the following Cartesian coordinates to the cooresponding polar coordinates using positive r. (i) `(1,-1)` (ii) `(-3,-4)`

2 Answers 5 Views

In the `DeltaABC`, the coordinates of B are `(0, 0), AB=2, /_ABC=pi/3` and the middle point of BC has the coordinates (2,0). The centroid of the trian

2 Answers 5 Views

Two charges `-2Q` abd `Q` are located at the points with coordinates `(-3a, 0)` and `(+3a, 0)` respectively in the x-y plane. (i) Show that all points

2 Answers 4 Views

If (4, -3) and (-4, 3) are the coordinates of the ends of the diameter of the circle, then the coordinates of centre of the circle are

2 Answers 5 Views

If (6, -8) and (-6, 8) are the coordinates of the ends points of the diameter of a circle, then the coordinates of the centre of the circle are –

2 Answers 4 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

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