$A$ ball at point '$O$' is at a horizontal distance of $7 \ m$ from a wall. On the wall,a target is set at point '$C$'. If the ball is thrown from '$O$' at an angle $37^{\circ}$ with the horizontal,aiming at the target '$C$',but it hits the wall at point '$D$',which is at a vertical distance '$y_0$' below '$C$'. If the initial velocity of the ball is $15 \ m/s$,find $y_0$ (given $\cos 37^{\circ} = \frac{4}{5}$). (in $m$)

$A$ ball can be thrown to a maximum horizontal distance of $100\,m$. To what maximum height can it be thrown?

$A$ stone is thrown vertically at a speed of $30 \,ms^{-1}$ making an angle of $45^{\circ}$ with the horizontal. What is the maximum height reached by the stone (in $\,m$)? Take $g=10 \,ms^{-2}$.

If $x$ and $y$ coordinates of a projectile as a function of time are given as $24t$ and $43.6t - 4.9t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2 \text{ s}$ is . . . . . . .

Four projectiles are fired with the same velocities at angles $25^{\circ}, 40^{\circ}, 55^{\circ}$ and $70^{\circ}$ with the horizontal. The range of the projectile will be largest for the one projected at angle $.......$ . (in $^{\circ}$)

In the climax of a movie,the hero jumps from a helicopter and the villain chasing the hero also jumps at the same time from the same level. After some time,when they are at the same horizontal level,the villain fires a bullet horizontally towards the hero. Both the hero and the villain are falling with a constant downward acceleration of $2\ m/s^2$ due to their parachutes. Assuming the hero is within the range of the bullet and air resistance on the bullet is negligible,which of the following is correct?