Show that a boat must move at an angle with respect to river water in order to cross the river in minimum time .

Crossing River In Minimum Time

A boat can be rowed at 5 m/s on still water. It is used to cross a 200m wide river from the south bank to the north bank. The river current has uniform velocity of 3 m/s due east. (a) In which direction must it be steered to cross the river perpendicular to current ? (b) How long will it take to cross the river in a direction perpendicular to the river flow ? (c) In which direction must the boat be steered to cross the river in minimum time ? How far will it drift ?

A boat can be rowed at 5 m/s on still water. It is used to cross a 200m wide river from the south bank to the north bank. The river current has uniform velocity of 3 m/s due east. (a) In which direction must it be steered to cross the river perpendicular to current ? (b) How long will it take to cross the river in a direction perpendicular to the river flow ? (c) In which direction must the boat be steered to cross the river in minimum time ? How far will it drift ?

A boat can be rowed at 5 m/s on still water. It is used to cross a 200m wide river from the south bank to the north bank. The river current has uniform velocity of 3 m/s due east. (a) In which direction must it be steered to cross the river perpendicular to current ? (b) How long will it take to cross the river in a direction perpendicular to the river flow ? (c) In which direction must the boat be steered to cross the river in minimum time ? How far will it drift ?

A boat is moving with a velocity (3hati +hatj) with respect to ground. The water in the river is moving with a velocity -3hati - 4hatj with respect to ground. What is the relative velocity of boat with respect to river ?

sqrt(3) times the velocity of a boat on still water is twice the velocity of current of a river. At what angle , with respect to the current, should the boat be steered so as to cross the river in least distance ?

A man wishes to cross a river which is flowing at a certain speed . Man uses a motor boat whose velocity with respect to water is more than speed of flow. Minimum possible time the boat takes to cross the river is t_(1) , but drift along the length of river is x . When boat takes shortest route to cross the river , then it takes time t_(2) . Find the velocity of boat with respect to water .