Physics Assignment. Work sheet Brainy app give its diagram. The current in a river is acting downstream with a magnitude 5km/h. A man rowing at 3km/h heads the boat at an angle of 45 degrees with the downstream direction of the river bank. (a). Draw a vector diagram showing the velocities of the current and the boat and thus the resultant velocity of the boat when the current is taken into account. (b)..Find the exact magnitude and the direction of the resultant velocity.

2. Draw a vector representing the boat's velocity at an angle of 45 degrees upstream from the current direction (towards the positive y-direction) with a magnitude of 3 km/h.

3. Use the parallelogram method to find the resultant velocity by adding the two vectors.

(b) Magnitude and Direction of the Resultant Velocity:

1. Resolve the boat's velocity into components:

- Downstream component (Vbx) = 3 cos(45°) ≈ 2.12 km/h

- Perpendicular component (Vby) = 3 sin(45°) ≈ 2.12 km/h

2. The resultant velocity (Vr) is the vector sum of the current and the boat's velocity components:

- Vr = √(Vbx² + Vby² + Vc²) = √(2.12² + 2.12² + 5²) ≈ 5.83 km/h

3. The direction of the resultant velocity is given by:

- θ = tan⁻¹(Vby / (Vc + Vbx)) ≈ tan⁻¹(2.12 / (5 + 2.12)) ≈ 22.5°

The key steps are:

1. Representing the current and boat's velocity as vectors in the vector diagram.

2. Resolving the boat's velocity into downstream and perpendicular components.

3. Calculating the magnitude of the resultant velocity using vector addition.

4. Determining the direction of the resultant velocity using trigonometry.