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 swimmer's speed in still water is 20 m/s. A river flows due 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?

If ${\rm{\vec A}} + {\rm{\vec B}} = {\rm{\vec C}}\,and\,A = \sqrt 3 ,\,B = \sqrt 3 \,and\,C = 3$, then the angle between ${\rm{\vec A}}\;and\;{\rm{\vec B}}$ is

A boat can travel at a speed of 8 kmph in still water on a lake. In the flowing water of a stream, it can move at 8kmph relative to the water in the stream. If the stream speed is 3kmph, how fast can the boat move past a tree on the shore in travelling (i) upstream (ii) downstream?

A swimmer can swim at 25 m/s in still water. A river flows due north at 15 m/s. To cross the river from east to west along the shortest path, what should be the swimmer's velocity component directed towards west?

A boat capable of a speed $v$ in still water wants to cross a river of width $d$ flowing with speed $u$. If the boat crosses the river in minimum time, the drift along the river is:

A boat can travel at a speed of 10 km/h in still water. If the river flows at 4 km/h, what is the speed of the boat downstream?

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t. north is given by:

A boat can travel at 12 m/s in still water. A current flows west at 4 m/s. If the boat starts from the north bank and aims to cross a river to the south bank via the shortest path, what angle with respect to south should the boat's heading be?

A boat crosses a river of width $d$ flowing with speed $u$. The boat can travel with speed $v$ in still water. If the boat heads at an angle $heta$ with respect to the perpendicular to the river flow such that it reaches the directly opposite point on the other bank, the time taken to cross the river is:

A swimmer's speed in still water is 15 m/s. A river flows due east at 5 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?