Question

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.)

Answer 1

v = √ (v₁² - vₓ²)

θ = sin⁻¹ (vₓ / v₁)

Step-by-step 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)