In 3h24min, aballoon drifts 8.7kmnorth,9.7km east and 2.9km

To determine the overall displacement of the balloon after drifting for 3 hours and 24 minutes, we can break down its movement into components and then use the Pythagorean theorem to find the resultant distance. The balloon has moved in two horizontal directions (north and east) and has also ascended vertically. Let's analyze this step by step.

Breaking Down the Movement

The balloon's journey can be summarized as follows:

• Northward Movement: 8.7 km
• Eastward Movement: 9.7 km
• Vertical Movement: 2.9 km

Calculating Horizontal Displacement

First, we need to find the horizontal displacement, which is the combination of the northward and eastward movements. We can visualize this as a right triangle where:

• The northward distance (8.7 km) is one leg of the triangle.
• The eastward distance (9.7 km) is the other leg.

Using the Pythagorean theorem, we can calculate the horizontal displacement:

Horizontal Displacement (D_horizontal):

D_horizontal = √(8.7² + 9.7²)

D_horizontal = √(75.69 + 94.09)

D_horizontal = √(169.78)

D_horizontal ≈ 13.0 km

Incorporating Vertical Displacement

Now, we need to consider the vertical displacement of 2.9 km. This adds another dimension to our displacement calculation. We can again apply the Pythagorean theorem, this time to include the vertical component:

Total Displacement (D_total):

D_total = √(D_horizontal² + vertical²)

D_total = √(13.0² + 2.9²)

D_total = √(169 + 8.41)

D_total = √(177.41)

D_total ≈ 13.3 km

Final Result

The overall displacement of the balloon after drifting for 3 hours and 24 minutes is approximately 13.3 km, taking into account its movement north, east, and upward. This calculation illustrates how we can combine different types of movement to find a single resultant displacement, which is essential in physics and navigation.