A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point C starting from A. He swims with a speed of 5 km/hr, at an angle $θ$ w.r.t. the river flow. If $AB = BC = 400 m$ , then find the value of $θ$ (in degree).
Give the answer as the nearest integer.

Question

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point C starting from A. He swims with a speed of 5 km/hr, at an angle $θ$ w.r.t. the river flow. If $AB = BC = 400 m$ , then find the value of $θ$ (in degree).

River flows right; A is directly across from B, C is 400 m downstream from B

Give the answer as the nearest integer.

TestHub · Accepted Answer

AB and BC are equal, so the resultant velocity points at 45° to the bank.

Resolve the swimmer velocity along and across the river.

$v_{x} = 1 + 5 cos θ$

$v_{y} = 5 sin θ$

$v_{x} = v_{y}$

$1 + 5 cos θ = 5 sin θ$

At θ = 53°, sin θ = 4/5 and cos θ = 3/5.

$1 + 5 (3/5) = 4$

$5 (4/5) = 4$

$θ = 5 3^{\circ}$

Physics - Kinematics Question with Solution | TestHub

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