A motorboat whose speed in still water is $v$ km/h must aim upstream at an angle $heta$ with respect to the shore to travel directly across a river flowing at $u$ km/h. Which of the following is the correct expression for $\sin heta$?

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 man can row a boat in still water with a velocity of 8 kmph . Water is flowing in a river with a velocity of 4 kmph . At what angle should he row the boat so as to reach the exact opposite point

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

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 person can swim at a speed of 4 m/s in still water. They want to cross a river flowing east at 2 m/s. If they start from the south bank and want to reach a point directly north on the opposite bank, what angle west of north should they swim?

A boat crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water is 3 km/h. What is the velocity of the boat with respect to water?

An airplane flies at an airspeed of 250 km/h. There is a wind blowing from the west at 50 km/h. If the pilot wants to fly due north, what heading (angle with respect to north) should they take?

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 with a speed of 10 m/s in still water. If the river flows steadily at 5 m/s, what is the shortest time it takes the boat to cross a river 500 m wide?

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