Scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. The temperature of the gaseous planet increases linearly with the height of the atmosphere as measured from the top of a visible boundary layer, defined as 0 kilometers in altitude. The instruments on board can withstand a temperature of 601 K. At what altitude will the probe's instruments fail?

From my research, the image supports the question. From the graph given, we can construct the equation of the line using the two-point formula. Using the given value of 601 K, we can solve for the missing value of altitude.

y - y1 = [(y2 - y1)/(x2 - x1)](x- x1)
y - 147.52 = [ (567 - 147.54)/(78.11 - 18.4) ](x - 18.4)

Substituting y = 601 to solve for x:
601 - 147.52 = [ (567 - 147.54)/(78.11 - 18.4) ](x - 18.4)
x = 83

Therefore, the probe's instruments will fail at 83 kilometers.

onyebuchinnaji onyebuchinnaji · Answer 2 · 2022-05-25T12:20:53+02:00

At a temperature of 601 K, the altitude of the probe's instruments will fall at 83 km.

What is the value of the altitude?

The altitude of the probe is determined using method of interpolation as shown below;

601 K ------ x

567 K ---- 78.11 km

147.54 K ------ 18.4 km

we form equation as follows;

(601 - 567)/(567 - 147.54) = (x - 78.11) / (78.11 - 18.4)

34/419.46 = (x - 78.11) /59.71

0.081 = (x - 78.11) /59.71

x - 78.11 = 0.081(59.71)

x - 78.11 = 4.84

x = 82.95 km

x ≈ 83 km

Thus, at a temperature of 601 K, the altitude of the probe's instruments will fall at 83 km.

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