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 $g =10\,ms ^{-2}$ )
$\tan ^{-1} \frac{2}{3}$
$\tan ^{-1} \frac{3}{2}$
$\tan ^{-1} \frac{7}{4}$
$\tan ^{-1} \frac{4}{5}$
If a particle takes $t$ second less and acquires a velocity of $v \ ms^{^{-1}}$ more in falling through the same distance (starting from rest) on two planets where the accelerations due to gravity are $2 \,\, g$ and $8 \,\,g$ respectively then $v=$
The figure shows the velocity and the acceleration of a point like body at the initial moment of its motion. The direction and the absolute value of the acceleration remain constant. Find the time when the speed becomes minimum.........$s$ (Given : $a = 4\, m/s^2, v_0 = 40\, m/s, \phi =143^o$)
The equation of a projectile is $y=a x-b x^2$. Its horizontal range is ......
$List I$ describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figure. $List II$ gives possible magnitudes of then relative velocities (in $ms ^{-1}$ ) at time $t=\frac{\pi}{3} s$.
Which one of the following options is correct?