Final answer:
The boat's velocity relative to the river and the speed of the current can be calculated using the Pythagorean theorem and the inverse tangent function.
Step-by-step explanation:
The boat's velocity relative to the river can be calculated using the Pythagorean theorem, as the magnitude of the velocity vector is given by the sum of the squares of the boat's velocity and the river's velocity. In this case, the boat's velocity is 0.75 m/s in the y-direction and the river's velocity is 1.20 m/s to the right:
Vtot = sqrt((Vboat)^2 + (Vriver)^2) = sqrt((0.75)^2 + (1.20)^2) = 1.42 m/s
The direction of the boat's velocity relative to an observer on the shore can be found using the inverse tangent function: tan^-1(Vy/Ux). In this case, Vy is 0.75 m/s and Ux is 1.20 m/s:
tan^-1(0.75/1.20) = 33.70 degrees
Therefore, the total velocity of the boat is 1.42 m/s at an angle of 33.70 degrees relative to the shore.