Final answer:
The resulting speed of the powerboat is 47.13 kph, and the resulting direction is 4.32 degrees north of west.
Step-by-step explanation:
To find the resulting speed and direction of the powerboat, we need to consider the velocity of the powerboat in still water and the velocity of the river flow.
The velocity of the powerboat is given as 47 kph westward, while the velocity of the river is 3.5 kph northwestward.
To find the resulting speed, we can use the Pythagorean theorem.
The resulting speed is the square root of the sum of the squares of the velocities in the x and y directions.
The x-direction represents the westward direction, and the y-direction represents the northward direction.
Therefore, the resulting speed is calculated as follows:
Resulting speed = sqrt((47)^2 + (3.5)^2)
= sqrt(2209 + 12.25)
= sqrt(2221.25)
= 47.13 kph.
To find the resulting direction, we can use trigonometry.
The resulting direction is the angle that the resulting velocity makes with the positive x-axis or westward direction. Therefore, the resulting direction is given by:
Resulting direction = arctan(3.5/47)
= 4.32 degrees north of west.