Scientists released a weather balloon from a raised platform at 4:00 p.m. The weather balloon rose at a constant speed. At 4:05 pm, the weather balloon's altitude was 1,482 meters. At 4:09, the weather balloon had reached an altitude of 2,626 meters.

How many meters did the weather balloon rise each minute?
___

How high was the launch platform?
___

Complete the equation that describes the relationship between the altitude of the weather balloon in meters, A, and the elapsed time in minutes, t.
A = ___ t + ___

1 answer

To determine how many meters the weather balloon rose each minute, we can first calculate the elevation change between the two given times.

  1. Calculate the altitude increase:

    • At 4:05 p.m., the altitude was 1,482 meters.
    • At 4:09 p.m., the altitude was 2,626 meters.
    • The change in altitude is: \[ 2,626 \text{ m} - 1,482 \text{ m} = 1,144 \text{ m} \]
  2. Calculate the time elapsed:

    • From 4:05 to 4:09, 4 minutes elapsed.
  3. Calculate the rise per minute:

    • The rise per minute can be determined by dividing the change in altitude by the time elapsed: \[ \frac{1,144 \text{ m}}{4 \text{ min}} = 286 \text{ m/min} \]

So, the weather balloon rose 286 meters per minute.


Next, to determine how high the launch platform was, we need to find the altitude at t = 0 (when the balloon was released at 4:00 p.m.).

  1. Let’s establish a linear function based on the information we have: We know:

    • At t = 5 minutes (4:05 p.m.), A = 1,482 m
    • At t = 9 minutes (4:09 p.m.), A = 2,626 m.
  2. Using the rise rate we found (286 m/min):

    • The altitude A can be expressed as: \[ A = 286t + h \] where \( h \) is the height of the launch platform.
  3. Substituting the information into the equations: For t = 5: \[ 1,482 = 286(5) + h \implies 1,482 = 1,430 + h \implies h = 1,482 - 1,430 = 52 \text{ meters} \]

So, the height of the launch platform is 52 meters.


Finally, we can write the equation that describes the relationship between the altitude A of the weather balloon in meters and the elapsed time t in minutes.

Based on our calculations:

  • The rise rate is 286 meters per minute.
  • The height of the launch platform is 52 meters.

Thus, the equation is: \[ A = 286t + 52 \]

Final Answers:

  • The weather balloon rose 286 meters per minute.
  • The height of the launch platform was 52 meters.
  • The equation is \( A = 286t + 52 \).