A ferryboat traveling at a speed of 30 km/h attempts to cross a river with a current of 5 km/h. What is the boat's speed relative to the shore?

A.8 km/h
B.25 km/h
C.30.4 km/h
D.32.8 km/h

It depends upon whether the ferry is travelling straight across (but aimed upstream) or aimed straight across (but drifting downsteam). The question does not make clear which it is.

In the first case, the answer is sqrt(30^2 -5^2) = 29.6 mph
In the secnd case, the answer is sqrt(30^2 + 5^2) = 30.4 mph

32.8 km/h

To determine the boat's speed relative to the shore, we need to find the resultant speed by considering the effect of both the boat's speed and the river's current.

The boat's speed relative to the shore can be calculated using the concept of vector addition. We can treat the boat's speed and the river's current as two separate vectors and find their resultant vector, which represents the boat's speed relative to the shore.

To calculate the resultant vector, we can use the Pythagorean theorem for right triangles.

First, let's consider that the boat's speed of 30 km/h is the speed of the boat relative to the still water (without the river's current).

Next, we need to consider the effect of the river's current. Since the current is flowing perpendicular to the boat's direction (across the river), the current's speed does not directly add to or subtract from the boat's speed. Instead, it causes the boat to drift sideways.

Using the Pythagorean theorem, we can determine the resultant speed:

Resultant speed = √(boat's speed^2 + river current^2)

Resultant speed = √(30^2 + 5^2)

Resultant speed = √(900 + 25)

Resultant speed = √925

Resultant speed ≈ 30.4138 km/h

Therefore, the boat's speed relative to the shore is approximately 30.4 km/h.

Hence, the correct answer is option C: 30.4 km/h.