A boat is moving across a river at a speed of 8 km/h, while the river flows at 3

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What’s inside this PDF?

Question: A boat is moving across a river at a speed of 8 km/h, while the river flows at 3 km/h. What is the resultant speed of the boat relative to the riverbank?

Options:

5 km/h
8 km/h
9 km/h
11 km/h

Correct Answer: 9 km/h

Solution:

The resultant speed is found using the Pythagorean theorem: √(8^2 + 3^2) = √(64 + 9) = √73 ≈ 8.6 km/h.

A boat is moving across a river at a speed of 8 km/h, while the river flows at 3

Practice Questions

A boat is moving across a river at a speed of 8 km/h, while the river flows at 3 km/h. What is the resultant speed of the boat relative to the riverbank?

5 km/h
8 km/h
9 km/h
11 km/h

Questions & Step-by-Step Solutions

A boat is moving across a river at a speed of 8 km/h, while the river flows at 3 km/h. What is the resultant speed of the boat relative to the riverbank?

Step 1: Identify the speed of the boat across the river. This is given as 8 km/h.
Step 2: Identify the speed of the river's current. This is given as 3 km/h.
Step 3: Understand that the boat's speed and the river's speed are at right angles to each other. This means we can use the Pythagorean theorem to find the resultant speed.
Step 4: Use the Pythagorean theorem formula: Resultant speed = √(boat speed^2 + river speed^2).
Step 5: Substitute the values into the formula: Resultant speed = √(8^2 + 3^2).
Step 6: Calculate 8^2, which is 64, and 3^2, which is 9.
Step 7: Add these two results together: 64 + 9 = 73.
Step 8: Take the square root of 73 to find the resultant speed: √73.
Step 9: Calculate √73, which is approximately 8.6 km/h.

Relative Velocity – Understanding how to calculate the resultant speed of an object moving in two perpendicular directions.
Pythagorean Theorem – Applying the theorem to find the magnitude of the resultant vector from two perpendicular components.

A boat is moving across a river at a speed of 8 km/h, while the river flows at 3

What’s inside this PDF?

A boat is moving across a river at a speed of 8 km/h, while the river flows at 3

Practice Questions

Questions & Step-by-Step Solutions

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