A particle $(A)$ is dropped from a height and another particle $(B)$ is thrown in horizontal direction with speed of $5\; m/sec$ from the same height. The correct statement is
Both particles will reach at ground simultaneously
Both particles will reach at ground with same speed
Particle $(A)$ will reach at ground first with respect to particle $(B)$
Particle $ (B) $ will reach at ground first with respect to particle $(A)$
The coordinates of a particle moving in a plane are given by $x = a\cos (pt)$ and $y(t) = b\sin (pt)$ where $a,\,\,b\,( < a)$ and $p$ are positive constants of appropriate dimensions. Then
Velocity-time graph for a car is semicircle as shown here. Which of the following is correct :
The position of a projectile launched from the origin at $t=0$ is given by $\vec{r}=(40 \hat{i}+50 \hat{j}) m$ at $t=$ $2 s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (take $g =10\,ms ^{-2}$ )
Velocity of a particle moving in a curvilinear path in a horizontal $X$ $Y$ plane varies with time as $\vec v = (2t\hat i + t^2 \hat j) \ \ m/s.$ Here, $t$ is in second. At $t = 1\ s$
Three particles, located initially on the vertices of an equilateral triangle of side $L,$ start moving with a constant tangential acceleration towards each other in a cyclic manner, forming spiral loci that coverage at the centroid of the triangle. The length of one such spiral locus will be