Displacement in 2D

Q.

A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction

1. Due north

2. ${30}^{\circ }$ east of north

3. ${30}^{\circ }$ west of north

4. ${60}^{\circ }$ east of north

Q. A particle is moving in $xy-$plane with $y=\frac{x}{2}$ and velocity along $x$ direction is $u_x=4-2t$. The correct options are

1. Initial velocities of $x$ and $y$ directions are negative.
2. Initial velocities of $x$ and $y$ directions are positive.
3. Motion is first retarded, then accelerated
4. Motion is first accelerated, then retarded.