$A$ projectile is thrown with a velocity of $50 \, m/s$ at an angle of $53^o$ with the horizontal. Determine the instants at which the projectile is at the same height.

$A$ body of mass $m$ thrown up vertically with velocity $v_1$ reaches a maximum height $h_1$ in $t_1$ seconds. Another body of mass $2m$ is projected with a velocity $v_2$ at an angle $\theta$. The second body reaches a maximum height $h_2$ in time $t_2$ seconds. If $t_1 = 2t_2$, then the ratio $\left(\frac{h_1}{h_2}\right)$ is

$A$ projectile is given an initial velocity of $(\hat i + 2\hat j) \ ms^{-1}$,where $\hat i$ is along the ground and $\hat j$ is along the vertical. If $g = 10 \ m/s^2$,the equation of its trajectory is

$A$ projectile is projected at $30^{\circ}$ from horizontal with initial velocity $40\,m/s$. The velocity of the projectile at $t = 2\,s$ from the start will be $........$ (Given $g = 10\,m/s^2$)

For a projectile motion,the angle between the velocity and acceleration is minimum and acute at

$A$ boy throws a ball into the air at $45^{\circ}$ from the horizontal to land it on the roof of a building of height $H$. If the ball attains maximum height in $2 \text{ s}$ and lands on the building in $3 \text{ s}$ after launch, then the value of $H$ is . . . . . . $\text{m}$. $(g = 10 \text{ m/s}^2)$