Final answer:
The magnitude of the boat's resultant velocity is 15.8 m/s, and it will go towards his left at an angle of 18.4 degrees to a line drawn across the river.
Step-by-step explanation:
The resultant velocity of the boat can be found using vector addition. The magnitude of the boat's velocity is 15 m/s, and the magnitude of the river's velocity is 5 m/s. To find the magnitude of the resultant velocity, we can use the Pythagorean theorem: a^2 + b^2 = c^2. So in this case, 15^2 + 5^2 = c^2, which gives us c = sqrt(250) = 15.8 m/s.
The direction of the boat's resultant velocity can be found using trigonometry. Using the tangent function, we can find the angle: tan(theta) = opposite/adjacent = 5/15, which gives us theta = 18.4 degrees.
Therefore, the magnitude of the boat's resultant velocity is 15.8 m/s and it will go towards his left at an angle of 18.4 degrees to a line drawn across the river.