A river of width with straight parallel banks flows due north with speed

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

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

OX

and

OY

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

u=x(a-x)\frac{v}{a^2}

, find: (1) The equation of trajectory of the boat. (2) The time taken to cross the river. (3) The absolute velocity of the boatman when he reaches the opposite bank. (4) The displacement of the boatman from the initial position when he reaches the opposite bank.

Related theory

2D Motion with Constant Acceleration
Relative Motion & Reference Frames
Reference frames and point mass
Motion in a plane

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