$A$ bullet must be fired from a height of ........ $cm$ to hit a target $100 \,m$ away. The horizontal velocity of the bullet is $500 \,ms^{-1}$. (Take $g = 10 \,ms^{-2}$)

Shots are fired from the top of a tower and from its bottom simultaneously at angles $30^o$ and $60^o$ as shown. If the horizontal distance of the point of collision is at a distance $a$ from the tower,then the height of the tower $h$ is:

$A$ plane is flying horizontally at $98 \, m/s$ and releases an object which reaches the ground in $10 \, s$. The angle made by the object with the horizontal while hitting the ground is ......... $^o$.

$A$ ball of mass $m=1 \, kg$ is thrown from the top of a building with initial velocity $v=(20 \, m/s) \hat{i} + (24 \, m/s) \hat{j}$ at time $t=0$. The change in the potential energy of the ball between $t=0$ and $t=6 \, s$, if the ball does not hit the ground, is (assume $g=10 \, m/s^2$): (in $ \, J$)

$A$ stone is projected from a point on the ground so as to hit a bird on the top of a vertical pole of height $h$ and then attain a maximum height $2h$ above the ground. If at the instant of projection the bird flies away horizontally with a uniform speed and if the stone hits the bird while descending,then the ratio of the speed of the bird to the horizontal speed of the stone is

$A$ player throws a ball that reaches another player in $4\,s$. If the height of each player is $1.5\,m$,the maximum height attained by the ball from the ground level is .......... $m$.