The Question is from NEET guide , and it was created by the author P.NARASIMHA

Question

A swimmer can swim at a speed of $v$ in still water. He wants to cross a river flowing with speed $u$.  If the width of the river is $d$ and the swimmer crosses the river in minimum time, what is the drift experienced by the swimmer?

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: Option C
## CONCEPT FRAMEWORK
	**Primary Concept**: Relative Motion
	**Related Topics**: Vector addition, Kinematics
	**Prerequisites**: Understanding of relative velocities and time calculations in two dimensions.
## SOLUTION PATHWAY
**Given Information**:
	* Swimmer's speed in still water: $v$
	* River's speed: $u$
	* Width of the river: $d$
	* Condition: Swimmer crosses the river in minimum time
**Method & Steps**:
	1. To cross the river in minimum time, the swimmer must swim perpendicular to the river flow. This is because the time taken to cross the river depends solely on the component of the swimmer's velocity perpendicular to the river flow, and this component is maximized when the swimmer swims directly across.
		Reasoning: Time is minimized when the component of velocity perpendicular to the river is maximized.
		Formula/Rule: $t = \frac{distance}{velocity} $
	2. Calculate the time taken to cross the river.
		Working: Since the swimmer swims directly across with speed $v$, the time taken to cross the river is $t = \frac{d}{v}$
		Key Point: The swimmer's speed perpendicular to the river is $v$.
	3. Calculate the drift caused by the river flow.
		Result: The drift is the distance the swimmer travels downstream due to the river's current. Since the river flows with speed $u$, the drift is given by $drift = u 	imes t = u 	imes \frac{d}{v} = \frac{ud}{v}$
		Verification: The drift is in the direction of river flow, and the units are consistent (distance).
 ## OPTION ANALYSIS
[A] :x: This option represents the drift if the swimmer tried to cross the river directly opposite to starting point. 
[B] :x: This option represents no drift which isn't the case here. 
[C] ✓: This option correctly represents the drift experienced by the swimmer when they swim to minimize time.
[D] :x: This option represents the width of the river, and not the drift.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. [Error 1]: Confusing minimum time with shortest path. Minimum time is achieved when the swimmer swims perpendicular to river flow, whereas shortest path requires angling the swim.
		2. [Error 2]: Forgetting to consider the effect of river flow on the swimmer's horizontal displacement.
	**Quick Tips**:
		1. Minimum time is always achieved by swimming perpendicular to the flow.
		2. Drift is the product of the river's speed and the time taken to cross the river.

P.NARASIMHA · Answer

$\frac{vd}{u}$

P.NARASIMHA · Answer

0

P.NARASIMHA · Answer

The correct Option is "$\frac{ud}{v}$"

P.NARASIMHA · Answer

$d$

NEET Questions

Select Subject

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company