Question

A radius vector of poin $A$ relative to the origin varie with time $t$ as $\overrightarrow{r}=at\hat{i}-b{t}^2\hat{j}$ where $a$ and $b$ are constants. Find the equation of point's trajectory.

• A. $y=\frac{-4b}{a^2}{x}^2$
• B. $y=\frac{-2b}{a^2}{x}^2$
• C. $y=\frac{-b}{a^2}{x}^2$
• D. $y=\frac{-b}{2a^2}{x}^2$

Answer 1

Answer: (C)

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

Given radius vector is $\overrightarrow{r}=at\hat{i}-b{t}^2\hat{j}$

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

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