Q 11-03-147JEE MainJEE Main 2020 (8 Jan, Shift 1)Easy
A particle is moving along the $x$-axis with its coordinate with time $t$ given by $x(t) = 10 + 8t - 3t^2$. Another particle is moving along the $y$-axis with its coordinate as a function of time given by $y(t) = 5 - 8t^3$. At $t = 1$ s, the speed of the second particle as measured in the frame of the first particle is given as $\sqrt v$. Then $v$ (in m s$^{-1}$) is ______.
Numerical value type. Enter your answer.
Answer: 580
At $t = 1$ s:
First particle: $v_x = 8 - 6t = 2$ m/s along $x$.
Second particle: $v_y = -24t^2 = -24$ m/s along $y$.
Relative velocity: $\vec v_{21} = -2\hat i - 24\hat j$, so its speed is $\sqrt{4 + 576} = \sqrt{580}$.
So $v = 580$.
Solution by Sreeraj P, M.Sc Physics