A swimmer can swim with a velocity of $v$ m/s in still water. He wants to cross a river of width $d$ meters flowing with a velocity $u$ m/s. If the swimmer heads in a direction making an angle $heta$ with the upstream direction such that he crosses the river in minimum time, what is the drift experienced by the swimmer?

A swimmer can swim at a speed of 4 m/s in still water. A river flows south at 2 m/s. The swimmer wants to cross the river from the west bank to the east bank and arrive directly across from their starting point. What angle east of north should the swimmer aim?

A swimmer's speed in still water is 20 m/s. The river flows east at 10 m/s. If the swimmer starts on the south bank and wants to cross via the shortest path, at what angle with respect to north should they swim?

A boat can travel with a speed of 10 km/h in still water. If the speed of the river is 4 km/h, what is the shortest time taken by the boat to cross a river of width 1 km?

A boat's speed in still water is $v_b$ and the river flows with speed $v_r$. If the boat is steered at an angle $heta$ with respect to the river flow, what is the boat's resultant speed relative to the ground?

A boatman can row with a speed of $10$ km/h in still water. If the river flows steadily at $5$ km/h, in which direction should he row his boat in order to reach a point on the other bank directly opposite to the point from where he started? The width of the river is $2$ km.

A car is travelling at a velocity of $10{\rm{\;km}}{{\rm{h}}^{ - 1}}$ on a straight road. The driver of the car throws a parcel with a velocity of $10\sqrt 2 {\rm{\;km}}{{\rm{h}}^{ - 1}}$ when the car is passing by a man standing on the side of the road. If the parcel is to reach the man, the direction of throw makes the following angle with direction of the car

The sum of the magnitudes of two forces acting at a point is 16 N. the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N. If the smaller force is magnitude x, then the value of x is

A motorboat's speed in still water is 25 km/h. A river flows south at 5 km/h. If the boat starts on the west bank and wants to cross the river in the shortest time, what angle east of north should the boat's heading be?

A body starts from rest from the origin with an acceleration of $6\;m/{s^2}$ along the x-axis and $8\;m/{s^2}$ along the y-axis. Its distance from the origin after 4 seconds will be

A boat can travel at 12 km/h in still water. A river flows due west at 4 km/h. If the boat needs to cross the river from the north bank to the south bank in the shortest time, what angle with respect to south should the boat be steered?