A man uses a boat to cross the river if the velocity of a boat is 8 km/h and the resultant velocity by which boat crosses the river is 10 km/h then what is the velocity by which river is flowing?

Question

Question

Answer 1

CONCEPT:

Parallelogram Law of Vector Addition: It is used to add two vector quantities.

F1 JItendra.K 11-05-21 Savita D3

R² = A² + B² +2ABcosθ

where A and B are the two vector quantity; θ = Angle between two vector quantity

tan α = (Bsinθ)/(A + Bcosθ)

where α is the angle between the resultant and the vector

CALCULATION:

Given:

F1 JItendra.K 11-05-21 Savita D4

V_B = 8 Km/h; V_B_R = 10 Km/h

Where V_B = Velocity of a boat; V_B_R = Resultant velocity of boat and river; V_R = Velocity of river

The angle between the velocity of the river and the velocity of the boat is 90°; θ = 90°

By Parallelogram Law of Vector Addition

V_BR² = V_B² + V_R² + (2V_BV_Rcosθ)

10² = 8² + V_R² + (2 × 8 × V_R × cos(90°))

V_R² = 100 - 64

V_R = 6 Km/h

Hence option 1 is correct.

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