$A$ bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane,the trajectory of the bomb is a:

Two particles having position vectors $r_1 = (3 \hat{i} + 5 \hat{j}) \text{ m}$ and $r_2 = (-5 \hat{i} - 3 \hat{j}) \text{ m}$ are moving with velocities $v_1 = (4 \hat{i} + 3 \hat{j}) \text{ m/s}$ and $v_2 = (a \hat{i} + 7 \hat{j}) \text{ m/s}$. If they collide after $2 \text{ s}$,then the value of $a$ is:

$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \, km/h$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the moving man will be:

$A$ man is running on a level road with a speed of $10 \ m/s$. He feels that the rain is falling vertically downward with a speed of $10 \sqrt{3} \ m/s$. If he runs in the opposite direction with the same speed,then the speed of the rain relative to him will be:

$A$ man sitting in a bus travelling from west to east with a speed of $40 \, km/h$ observes that the rain-drops are falling vertically down. To another man standing on the ground,the rain will appear:

$A$ glass windscreen,whose inclination with the vertical can be changed,is mounted on a car. The car moves horizontally with a speed of $2\,m/s$. At what angle $\alpha$ with the vertical should the windscreen be placed so that the rain drops falling vertically downwards with velocity $6\,m/s$ strike the windscreen perpendicularly?