A particle $A$ is projected vertically upwards. Another particle $B$ is projected at an angle of $45^{\circ}$. Both reach the same height. The ratio of the initial kinetic energy of $A$ to that of $B$ is

$A$ ball is projected vertically upwards. Air resistance  variation in $g$ may be neglected. The ball rises to its maximum height $H$ in a time $T$, the height being $h$ after a time $t$

$[1]$ The graph of kinetic energy $E_k$ of the ball against height $h$ is shown in figure $1$

$[2]$ The graph of height $h$ against time $t$ is shown in figure $2$

$[3]$ The graph of gravitational energy $E_g$ of the ball against height $h$ is shown in figure $3$

Which of $A, B, C, D, E$ shows the correct answers?

A ball is projected from ground at an angle of $\theta $ from horizontal then graph of kinetic energy and time will be

A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$, then its velocity at $x=12 \,m$ is .............. $m / s$

particle is projected from level ground. Its kinetic energy $K$ changes due to gravity so $\frac{{{K_{\max }}}}{{{K_{\min }}}} = 9$. The ratio of the range to the maximum height attained during its flight is

A vehicle of mass $m$ is moving on a rough horizontal road with momentum $P$. If the coefficient of friction between the tyres and the road be $\mu$, then the stopping distance is