A river is flowing steradily with a speed ` 5 km h^(-1)` . A boat man can row with a speed of ` 10 km h^(-1)` in still water. He rows his boat in river at right angles to the bank of river, If width of river is ` 800 m`, (i) how much time the boat man will take to cross the river ? (ii) How far away from a point just opposite to the bank of river he will be reaching there ? (ii) What will be his effective speed gt

Explanation

Refer to Fig. 2 ( c) . 85,
.
Velocity of river flow, ` vec v_r = vec (OA)`,
wher ` v_r = 5 km h^(-1)`
Velocity of boat man , ` vec _b = vec (OB)` ,
where` v_v = 10 km h^(-1)` ltbRgt (i) Time taken by boat man to cross the river
` t= (OD)/v_b= (0.8km)/(10 km h^(-1)) = 0.08 h` ltbRgt `= 0.08 xx 60 min = 4.8 min` ltbRgt (ii) Distance ` DE= v_r xx t = 5 ( km h^(-1) xx 0.08 h` ltbRgt `= 0.40 km 400 m`
(iii) Resultant velocity of boat man
` v = sqrt (v-r^2 +v_b^2 ) = sqrt( 5^2 + 10^2)= 5 sqrt 5 km h^(-1)` ltbRgt The boat will row along (OC) andreaches the opposite bank at point (E).