A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
Practice Questions
1 question
Q1
A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
8 km/h
10 km/h
14 km/h
6 km/h
Speed of boat relative to riverbank = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km/h.
Questions & Step-by-step Solutions
1 item
Q
Q: A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
Solution: Speed of boat relative to riverbank = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km/h.
Steps: 10
Step 1: Identify the speed of the boat relative to the water, which is 8 km/h.
Step 2: Identify the speed of the river current, which is 6 km/h.
Step 3: Understand that the boat's speed and the river's speed form a right triangle, where the boat's speed is one side and the river's speed is the other side.
Step 4: Use the Pythagorean theorem to find the resultant speed of the boat relative to the riverbank. The formula is: Speed = √(boat speed² + river speed²).
Step 5: Substitute the values into the formula: Speed = √(8² + 6²).
Step 6: Calculate 8², which is 64.
Step 7: Calculate 6², which is 36.
Step 8: Add the two results: 64 + 36 = 100.
Step 9: Take the square root of 100, which is 10.
Step 10: Conclude that the speed of the boat relative to the riverbank is 10 km/h.
