To calculate the velocity of the child, we need two key pieces of information:

1. The displacement of the child (the straight-line distance between their starting and ending points).
2. The total time taken for the motion.

Step 1: Find the displacement

The child follows this path:

• 89 meters east,
• 56 meters north,
• 34 meters south,
• 89 meters west.

To find the displacement, we calculate how far the child is from their starting point at the end of their journey.

• After moving 56 meters north and then 34 meters south, the net vertical movement is: $56 \, \text{meters} - 34 \, \text{meters} = 22 \, \text{meters north}.$

• After moving 89 meters east and 89 meters west, the net horizontal movement is: $89 \, \text{meters} - 89 \, \text{meters} = 0 \, \text{meters}.$

So, the child ends up 22 meters north of their starting point.

Thus, the displacement is 22 meters north.

Step 2: Find the velocity

The velocity is the displacement divided by the total time.

Given:

• Displacement = 22 meters,
• Time = 7 minutes = $7 \times 60 = 420$ seconds.

Now, calculate the velocity: $\text{Velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{22 \, \text{meters}}{420 \, \text{seconds}} \approx 0.0524 \, \text{meters per second}.$

Final Answer:

The velocity of the child is approximately $0.0524 \, \text{m/s}$, directed north.

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Would you like more details or have any questions?

Here are 5 related questions:

1. How is velocity different from speed in this context?
2. How would you calculate the total distance traveled instead of the displacement?
3. What would the velocity be if the child had a different time of 5 minutes?
4. What is the significance of direction in calculating velocity?
5. How would you calculate the speed if the entire trip took 10 minutes?

Tip: Always remember that velocity includes both magnitude and direction, while speed is only the magnitude of movement.