$A$ projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80\,m/s$. Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly $........\,m/s$.

$A$ stone is projected vertically upwards with velocity $V$. Another stone of the same mass is projected at an angle of $60^{\circ}$ with the vertical with the same speed $V$. The ratio of their potential energies at the highest points of their journey is:

$A$ particle moves over a $xy$ plane with a constant acceleration $\vec{a} = (4.0 \, m \, s^{-2}) \hat{i} + (4.0 \, m \, s^{-2}) \hat{j}$. At time $t = 0$,the velocity is $\vec{v}_0 = (4.0 \, m \, s^{-1}) \hat{i}$. The speed of the particle when it is displaced by $6.0 \, m$ parallel to the $x$-axis is,

Choose the correct alternative$(s)$.

$A$ body is projected from the ground at an angle $\theta_1$ with the horizontal with kinetic energy $K$. What is the potential energy of the body when the velocity makes an angle $\theta_2$ with the horizontal?

What determines the nature of the path followed by a particle?