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A river of width a with straight paralle...

A river of width a with straight parallel banks flows due north with speed u. The points O and A are on opposite banks and A is due east of O. Coordinate axes `O_x` and `O_y` are taken in the east and north directions respectively. A boat, whose speed is v relative to water, starts from O and crosses the river. If the boat is steered due east and u varies with `x as : u = x(a-x) v/a^2.` Find
(a) equation of trajectory of the boat,
(b) time taken to cross the river,
(c) absolute velocity of boatman when he reaches the opposite bank,
(d) the displacement of boatman when he reaches the opposite bank from the initial position.

A

west

B

south

C

east

D

north

Text Solution

Verified by Experts

The correct Answer is:
C
When the boatman reaches the oppostie side, `x=a` or `v_(y)=0` (from eqution 1)
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