A projectile is thrown with some initial velocity at an angle $\alpha$ to the horizontal. Its velocity when it is at the highest point is $(2 / 5)^{1 / 2}$ times the velocity when it is at height half of the maximum height. Find the angle of projection $\alpha$ with the horizontal.

A bullet fired at an angle of $30^o$ with the horizontal hits the ground $3.0\; km$ away. By adjusting its angle of projection, can one hope to hit a target $5.0\; km$ away ? Assume the muzzle speed to be fixed, and neglect air resistance.

At what point of a projectile motion acceleration and velocity are perpendicular to each other

A very broad elevator is going up vertically with a constant acceleration of $2\,m / s ^2$. At the instant when its velocity is $4\,m / s$ a ball is projected from the floor of the lift with a speed of $4\,m / s$ relative to the floor at an elevation of $30^{\circ}$. The time taken by the ball to return the floor is $..............\,s$ $\left(g=10\,m / s ^2\right)$

A projectile is thrown from a point in a horizontal plane such that the horizontal and vertical velocities are $9.8 \;ms ^{-1}$ and $19.6\; ms ^{-1}$. It will strike the plane after covering distance of ........ $m$

A ball is projected with a velocity, $10 ms ^{-1}$, at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be$............... ms ^{-1}$