The range of the projectile projected at an angle of $15^{\circ}$ with the horizontal is $50\,m$. If the projectile is projected with the same velocity at an angle of $45^{\circ}$ with the horizontal,then its range will be $........\,m$.

$A$ ball $A$ is projected vertically upwards with a certain initial speed $u$. Another ball $B$ of the same mass is projected at an angle of $30^{\circ}$ with the vertical with the same initial speed $u$. At the highest point,the ratio of the potential energy of ball $A$ to that of ball $B$ will be: $(\sin 90^{\circ}=1, \sin 60^{\circ}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}, \sin 30^{\circ}=\cos 60^{\circ}=\frac{1}{2})$

In projectile motion,the modulus of the rate of change of velocity is:

The range of a projectile for a given initial velocity is maximum when the angle of projection is $45^\circ$. The range will be minimum,if the angle of projection is ......... $^\circ$.

$A$ body is projected at an angle of $45^{\circ}$ from a point on the ground at a distance of $30 \,m$ from the foot of a vertical pole of height $20 \,m$. The body just crosses the top of the pole and strikes the ground at a distance $s$ from the foot of the pole on the other side. Then, $s$ is: (in $\,m$)

$A$ ball is projected in a manner such that its horizontal range is $n$ times the maximum height. Find the ratio of potential energy to kinetic energy at the maximum height.