Final answer:
The total velocity of a boat crossing a river against the current is the vector sum of its own velocity and the river's current, which results in a diagonal path relative to the shore. The magnitude and angle of the resultant velocity can be calculated using the Pythagorean theorem and arctangent function.
Step-by-step explanation:
The total velocity of a boat trying to cross a river is affected by the current of the river. If a boat attempts to head straight across a river at a velocity of 0.75 m/s (Vboat) but the river current flows to the right at 1.20 m/s (Vriver), the actual path of the boat will be diagonal relative to the shore due to these combined velocities.
To calculate the resultant velocity (Vtot), we can use the Pythagorean theorem as it is a right triangle situation:
Vtot = √(Vboat2 + Vriver2). Plugging in the values, Vtot = √(0.752 + 1.202) = √(0.5625 + 1.44) = √(2.0025) = 1.415 m/s (approximately).
The angle at which the boat will travel relative to its intended path straight across the river can be found using the arctangent function:
angle = atan(Vriver/Vboat). Therefore, angle = atan(1.20/0.75) which is approximately 58.0 degrees. The boat will therefore be heading at an angle of 58.0 degrees to a line drawn straight across the river.