Request a call back

Join NOW to get access to exclusive study material for best results

JEE Class main Answered

a boat moves with velocity which is n times less than the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting.    I din understand how dx/d theta=ud/v sec theta tan theta-d sec^2 theta like whr did the addition sec theta come from??? so pls explain tht
Asked by joanmaria916 | 17 Jul, 2023, 11:24: AM
Expert Answer
Let us consider that boat moves with velocity v in a direction that makes angle θ with a line along the breadth of river as shown in figure.

Velocity v of boat can be resolved as (i) ( v cosθ ) along the line parallel to breadth of river and ( v sinθ ) parallel to direction of river flow velocity u.

Time taken t to cross the river is

............... (1)

During this time t , boat drifts a distance x due to river flow

..................... (2)
It can be seen from eqn.(2) , drift is a function of angle θ .

Minimum drift can be determined by differentiating eqn.(2) with respect to θ and equating the derivative to zero.

If we equate ( dx/dθ ) = 0 , then we get

From above expression, we get , sinθ = (v/u) ,

Hence to get minimum drift , angle θ should be , θ = sin-1 ( v/ u )

If boat speed v = u/n , then θ = sin-1 ( 1/n )

Answered by Thiyagarajan K | 19 Jul, 2023, 08:37: PM
JEE main - Physics
Asked by somidiblesson162 | 13 Jun, 2024, 09:34: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by gbharat875 | 07 Jun, 2024, 07:15: AM
ANSWERED BY EXPERT
JEE main - Physics
Asked by chaudharyrakesh10312 | 19 May, 2024, 02:12: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by amanniju2 | 17 May, 2024, 09:00: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by bhargavreddynellaballi | 30 Apr, 2024, 08:18: AM
ANSWERED BY EXPERT
JEE main - Physics
Asked by ravichandraravula66 | 29 Apr, 2024, 11:20: AM
ANSWERED BY EXPERT
JEE main - Physics
Asked by Machinenineha | 27 Mar, 2024, 05:28: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by baskaranfathima83 | 21 Jan, 2024, 09:34: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by tripathiji9876good | 10 Jan, 2024, 04:22: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by meenu0000156 | 05 Jan, 2024, 12:05: PM
ANSWERED BY EXPERT