A swimmer heads for the opposite bank of a river. Make a sketch showing the swimmer's two velocities and the resultant velocity. (Assume the river flows in the +x direction and the opposite bank is in the +y direction.)

    v = √ (v₁² - vₓ²)

 θ = sin⁻¹ (vₓ / v₁)

Explanation:

This is a speed composition exercise in kinematics, in the adjoint we can see the swimmer with speed v₁ and the river with speed vₓ, the resulting speed is v

To find these values we can use the Pythagorean theorem

           v₁² = v² + vₓ²

           v = √ (v₁² - vₓ²)

the direction the swimmer should take is

           sin θ = vₓ / v₁

           θ = sin⁻¹ (vₓ / v₁)

total distance/total time

(85 + 82)/(5+3)

167/8

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