$A$ projectile is projected at $10 \ m/s$ by making an angle of $60^{\circ}$ to the horizontal. After some time,its velocity makes an angle of $30^{\circ}$ to the horizontal. Its speed at this instant is:

$A$ projectile has a range of $1.5 \ km$ when projected at an angle of $15^{\circ}$. Find the range of the projectile when it is projected at an angle of $45^{\circ}$ with the same velocity. (in $km$)

$A$ large number of bullets are fired in all directions with the same speed $u$. The maximum area of the ground on which these bullets spread is ($g$ - acceleration due to gravity).

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?

$A$ body is projected at an angle of $60^{\circ}$ with the horizontal such that the vertical component of its initial velocity is $40 \ m \ s^{-1}$. The magnitude of velocity of the projectile at one quarter of its time of flight is nearly (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

The velocity of a projectile is $(6\hat{i} + 8\hat{j}) \ m/s$. Its horizontal range is ........ $m$.