Relative Motion activity - Free Printable

Problem Analysis and Solution

The worksheet focuses on relative motion, which involves calculating the speed of one object relative to another. Let's solve each problem step by step.

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#### Problem 1:
Question: If a car passes you in the left lane going 90 km/hr north while you are driving 80 km/hr north, how fast is the car moving relative to your car?

- Given:
- Speed of the car passing you: \( 90 \, \text{km/hr} \) (north)
- Your speed: \( 80 \, \text{km/hr} \) (north)

- Relative Speed Calculation:
Since both cars are moving in the same direction (north), the relative speed is the difference between their speeds:
\[
\text{Relative Speed} = \text{Speed of Car} - \text{Your Speed}
\]
\[
\text{Relative Speed} = 90 \, \text{km/hr} - 80 \, \text{km/hr} = 10 \, \text{km/hr}
\]

- Answer: The car is moving at \( 10 \, \text{km/hr} \) relative to your car.

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#### Problem 2:
Question: What is the walker's speed from the observer's perspective?

- Given:
- Speed of the train: \( 40 \, \text{mph} \) (left to right)
- Speed of the walker relative to the train: \( 10 \, \text{mph} \) (right to left)

- Observer's Perspective:
The observer is stationary. To find the walker's speed relative to the observer, we need to consider the combined effect of the train's motion and the walker's motion relative to the train.

- The train is moving at \( 40 \, \text{mph} \) to the right.
- The walker is moving at \( 10 \, \text{mph} \) to the left relative to the train.

Since the walker is moving in the opposite direction to the train, we subtract the walker's speed from the train's speed:
\[
\text{Walker's Speed Relative to Observer} = \text{Train's Speed} - \text{Walker's Speed Relative to Train}
\]
\[
\text{Walker's Speed Relative to Observer} = 40 \, \text{mph} - 10 \, \text{mph} = 30 \, \text{mph}
\]

- Answer: The walker's speed from the observer's perspective is \( 30 \, \text{mph} \).

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#### Problem 3:
Question: What is the walker's speed with respect to the train?

- Given:
- Speed of the train: \( 40 \, \text{mph} \) (left to right)
- Speed of the walker relative to the observer: \( 30 \, \text{mph} \) (right to left)

- Walker's Speed Relative to the Train:
To find the walker's speed relative to the train, we need to account for the fact that the train is moving in the opposite direction to the walker.

- The train is moving at \( 40 \, \text{mph} \) to the right.
- The walker is moving at \( 30 \, \text{mph} \) to the left relative to the observer.

Since the walker is moving in the opposite direction to the train, we add the walker's speed to the train's speed:
\[
\text{Walker's Speed Relative to Train} = \text{Walker's Speed Relative to Observer} + \text{Train's Speed}
\]
\[
\text{Walker's Speed Relative to Train} = 30 \, \text{mph} + 40 \, \text{mph} = 70 \, \text{mph}
\]

However, upon re-evaluating the problem, it seems there might be a misunderstanding in the question's phrasing. The walker's speed relative to the train is already given as \( 10 \, \text{mph} \) in the diagram. This suggests that the walker's speed relative to the train is directly provided and does not require additional calculation.

- Answer: The walker's speed with respect to the train is \( 10 \, \text{mph} \).

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Final Answers:

1. \( \boxed{10 \, \text{km/hr}} \)
2. \( \boxed{30 \, \text{mph}} \)
3. \( \boxed{10 \, \text{mph}} \)