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?
8 km/h
25 km/h
30.4 km/h
32.8 km/h
It is sqrt(30^2 + 5^2)= 30.4 km/h
To find the boat's speed relative to the shore, we need to consider the effect of the river's current.
The boat's speed relative to the river can be calculated by subtracting the speed of the current from the boat's speed.
So, the boat's speed relative to the river is 30 km/h - 5 km/h = 25 km/h.
Since the boat is crossing the river, we can think of it as moving in a right triangle, with the boat's speed relative to the river as the horizontal leg and the current's speed as the vertical leg. The boat's speed relative to the shore is the hypotenuse of this triangle.
We can use the Pythagorean theorem to find the boat's speed relative to the shore. The formula is:
speed relative to the shore = √(speed relative to the river)^2 + (speed of the current)^2
In this case, the speed relative to the river is 25 km/h and the speed of the current is 5 km/h. Plugging these values into the formula:
speed relative to the shore = √(25 km/h)^2 + (5 km/h)^2
= √625 km^2/h^2 + 25 km^2/h^2
= √650 km^2/h^2
≈ 25.49 km/h
Therefore, the boat's speed relative to the shore is approximately 25.49 km/h, which can be rounded to 25 km/h.