A-river-of-width-d-is-flowing-with-speed-u-as-shown-in-the-figure-John-can-swim-with-maximum-speed-v-relative-to-the-river-and-can-cross-it-in-shortest-time-T-John-starts-at-A-B-is-the-point-direct

Question Number 19200 by Tinkutara last updated on 06/Aug/17

A river of width d is flowing with speed

u as shown in the figure . John can swim

with maximum speed v relative to the

river and can cross it in shortest time

T . John starts at A . B is the point

directly opposite to A on the other

bank of the river . If t be the time John

takes to reach the opposite bank, match

the situation in the column I to the

possibilities in column II .

Column I

(A) John reaches to the left of B

(B) John reaches to the right of B

(C) John reaches the point B

(D) John drifts along the bank while

minimizing the time

Column II

(p) t = T

(q) t > T

(r) u < v

(s) u > v

Commented by Tinkutara last updated on 06/Aug/17

Commented by ajfour last updated on 07/Aug/17

Commented by ajfour last updated on 07/Aug/17

To minimise the time, θ = 0

and john reaches to the right of B .

t = T = \frac{d}{v}; drift = \frac{ud}{v}

regardless of v > u or v < u .

If θ > 0 or θ < 0 \Rightarrow t = \frac{d}{vcos θ} > T

If John reaches left of B,

θ > \sin^{- 1} (\frac{u}{v}) and v > u, t > T

If time is to be minimised, John

{shouldn}^{'} t waste time drfting

along the bank .

(A) \to (q), (r)

(B) \to (p) or (q), (r) or (s)

(C) \to (q), (r)

(D) \to (q), (r) or (s)

Commented by Tinkutara last updated on 07/Aug/17

Thank you very much Sir!

Commented by ajfour last updated on 07/Aug/17

thanks .

Facebook Tweet Pin