As a probe approached a distant moon, Nova and Luna compared two descent plans on the control screen. Both graphs showed altitude in kilometers as a function of time in minutes. Plan A began at an altitude of 12 kilometers and decreased at a constant rate of 2 kilometers per minute, reaching altitude 0 at 6 minutes. Plan B also began at 12 kilometers, but after 4 minutes its altitude was still 6 kilometers. From that point, its graph became steeper and reached altitude 0 at 6 minutes. Luna noted that both plans had the same vertical intercept and landing-time intercept, but their rates of change behaved differently. Plan A provided a steady descent throughout the interval, while Plan B required a faster final drop. To avoid the sudden change in descent rate, Nova and Luna selected Plan A. The probe followed the steady path and landed at the planned time.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
The initial altitude is 12, and the altitude decreases by 2 for each minute.
Plan A begins at 12 kilometers and descends at a constant rate of 2 kilometers per minute. Which equation represents its altitude A after t minutes?
A = 12 + 2tA = 2t - 12A = 12 - 2tA = 12 - 6t
Correct! The initial value is 12 and the constant rate of change is -2 kilometers per minute.
Not quite. Use 12 as the initial altitude and a negative rate because the altitude is decreasing.
Next
🎉 Congrats! You got this question!
Hint
First use Plan A's equation to find its altitude at 4 minutes, then compare it with Plan B's altitude of 6 kilometers.
At t = 4 minutes, Plan B is at 6 kilometers. Plan A follows A = 12 - 2t. How many kilometers higher is Plan B than Plan A at t = 4 minutes?
Correct! Plan A is at 4 kilometers, so Plan B is 2 kilometers higher.
Try again. Find Plan A's altitude when t = 4, then subtract it from Plan B's altitude.
Next
🎉 Congrats! You got this question!
Hint
For Plan B, divide the change in altitude from 6 to 0 by the change in time from 4 to 6 minutes.
Plan B drops from 6 kilometers at t = 4 minutes to 0 kilometers at t = 6 minutes. Which comparison correctly explains why its final descent is steeper than Plan A's steady descent?
Plan B's final rate is -1 kilometer per minute, while Plan A's rate is -2 kilometers per minute.Plan B's final rate is -2 kilometers per minute, the same as Plan A's rate.Plan B's final rate is -6 kilometers per minute, while Plan A's rate is -2 kilometers per minute.Plan B's final rate is -3 kilometers per minute, while Plan A's rate is -2 kilometers per minute.
Correct! Plan B descends at -3 kilometers per minute during its final segment, which is a faster drop than Plan A's -2.
Not quite. Calculate Plan B's change in altitude over the 2-minute interval from t = 4 to t = 6.
Next
🎉🎉🎉🎉🎉🎉🎉🎉
🎉 Congrats! You finished this challenge set!
Sondanın Alçalma Planını Seçmek
TR
ARC_G10_PA_02_STORY_02
Sondanın Alçalma Planını Seçmek
Choosing the Probe's Descent
EN
ARC_G10_PA_02_STORY_02
Choosing the Probe's Descent