Relative motion Ques?

Question

i spent 4 hours on this Q,can u help me how i can got this result???

The banks of a river 40 m wide are parallel and A and B are points on opposite banks. The distance AB is 50 m and B is downstream of A. There is a constant current of 4 m/s flowing.

i.What is the minimum speed of the at which a motor boat must be able to move in still water in orderto cross the river from A to B?Answer 3.2m/s)

ii.If a boat sails from A to B with constant velocity in 7.5 s, find the speed of the boat and the direction at which it is steered?(ans 5/3m/s)
iii.Whilst this boat is sailing from A to B, a man runs across a bridge which is at right angles to the banks of the rivern. To this man, the boat appears o be traveling parallel to the river banks. Find the speed at which the man is running.(answer 5/3)

Answer 1

Q (i) The question asks to find out the minimum velocity of the boat to go from A to B in "still" water. If the implication is that there is no current then the question is incomplete as it gives only one parameter, the distance between the points

To go from A to B which are on the opposite banks, the boat must go along the current as well as across it. The minimum speed of the boat would be when it has no velocity of its own in the direction of the current.

The distance between A and B , along the banks and in the direction of the current, is (50^2 - 40^2) ^1/2 = 30 m. The current has a velocity of 4 m/s. Hence the time of travel of the boat in this direction is 30/4 = 7.5 sec. In this time the boat also goes across the river which is 40 m wide. The minimum velocity of the boat is therefore 40/7.5 = 5 1/3 m/s which is in the direction perpendicular to the current and the banks

Q (ii) The boat travels from A to B (50 m) in 7.5 sec, hence has a speed of 50/7.5 = 6 1/3 m/s. The velocity in the direction of the width(40 m) of the river is 40/7.5(time) =5 1/3 m/s. The boat moves in the direction of the current at a speed of 30/7.5 = 4 m/s. Since this is the speed of the current alone, the boat has no velocity of its own in this direction. The boat is therefore steered in a direction normal to the current (banks) with a speed of 5 1/3 m/s.

Q(iii) In order that the boat should appear to be moving parallel to the banks, the relative velocity between the man and the boat in the direction perpendicular to the banks must be nil. Therefore the man must run along the bridge with the same speed as that of the boat in the same direction i.e. normal to the banks. The required speed is 5 1/3 m/s.

Answer 2

1) now.. lets consider that the speed is Vmin
and the speed of river Vriver=4m/s
by diagram[i cant draw here]
Vmin = Vriver * sin40/50
Vmin = 4 * 40/50
Vmin = 3.2m/s

Answer 3

You really need to know how **far** downstream B is from A before you can work these problems.


Doug