Question

Path traced by a moving particle in space is called trajectory of the particle. Shape of trajectory is decided by the forces acting on the particle. When a coordinate system is associated with a particle's motion, the curve equation in which the particle moves $[y=f(x\left)\right]$ is called equation of trajectory. It is just giving us the relation among $x$ and $y$ coordinates of the particle i.e. the locus of particle. To find equation of trajectory of a particle, find first $x$ and $y$ co-ordinates of the particle as a function of time and eliminate the time factor. The position vector of car w.r.t. its starting point is given as $\overrightarrow{r}=at\hat{i}-b{t}^2\hat{j}$ where $a$ and $b$ are positive constants. The locus of a particle is

• A. $a^{2}y+b{x}^2=0$
• B. $a^{2}y=b{x}^2$
• C. $y=\frac{b}{a^2}x$
• D. $a{y}^2=b^{2}x$

Answer 1

Answer: (A)

$a^{2}y+b{x}^2=0$

Position vector of car w.r.t starting point (origin) $\overrightarrow{r}=at\hat{i}-b{t}^2\hat{j}$

$\therefore$ $x=at$ $⟹$ $t=\frac{x}{a}$

Also $y=-b{t}^2=-b\times \frac{x^2}{a^2}$

$⟹$ $a^{2}y+b{x}^2=0$