$A$ ball is projected upwards from the top of a tower with a velocity $50 \, m/s$ making an angle $30^\circ$ with the horizontal. The height of the tower is $70 \, m$. After how many seconds from the instant of throwing will the ball reach the ground? ........ $s$

$A$ 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$)

Two objects are located at a height of $10 \ m$ above the ground. At some point in time,the objects are thrown with an initial velocity of $2 \sqrt{2} \ m \ s^{-1}$ at an angle of $45^{\circ}$ and $135^{\circ}$ with the positive $X$-axis,respectively. Assuming $g = 10 \ m \ s^{-2}$,the velocity vectors will be perpendicular to each other at a time equal to: (in $s$)

An aeroplane is moving with a velocity $u$. It drops a packet from a height $h$. The time $t$ taken by the packet in reaching the ground will be

$A$ 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 $g = 10 \,ms^{-2}$)

$A$ 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