Avalanche forecasters measure the temperature gradientdT/dh, which is the rate at which the temperature of the snowpack T changes with respect to its depth h. If the temperature of the gradient is large, it may lead to a weak layer of snow in the snowpack. When these snow layers collapse, avalanches occur. Avalanche forecasters use the following rule: If dT/dh > 10˚C/meter anywhere in the snowpack, conditions are favorable for weak layer formation and the risk of avalanche. Assume that the temperature function T(h) is continuous and differentiable. a) An avalanche forecaster digs a snow pit and takes two temperature measurements. At the surface (h = 0) the temperature is -12˚C. At a depth of 1.1 meters, the temperature is 2˚C. Use these measurements and the Mean Value Theorem todetermine if the temperature gradient favors weak layer formation. Is there a risk of avalanche at this location? b) One mile away, another forecaster finds that the temperature at a depth of 1.4 meters is -1˚C, and at the surface the temperature is -12˚C. Use thesemeasurements and the Mean Value Theorem to determine if the temperature gradient favors weak layer formation. Is there a risk of avalanche at this location?
Avalanche forecasters measure the temperature gradient
dT/dh, which is the rate at which the temperature of the snowpack T changes with respect to its depth h. If the temperature of the gradient is large, it may lead to a weak layer of snow in the snowpack. When these snow layers collapse, avalanches occur.
Avalanche forecasters use the following rule: If dT/dh > 10˚C/meter anywhere in the snowpack, conditions are favorable for weak layer formation and the risk of avalanche. Assume that the temperature function T(h) is continuous and differentiable.
a) An avalanche forecaster digs a snow pit and takes two temperature measurements. At the surface (h = 0) the temperature is -12˚C. At a depth of 1.1 meters, the temperature is 2˚C. Use these measurements and the Mean Value Theorem todetermine if the temperature gradient favors weak layer formation. Is there a risk of avalanche at this location?
b) One mile away, another forecaster finds that the temperature at a depth of 1.4 meters is -1˚C, and at the surface the temperature is -12˚C. Use these
measurements and the Mean Value Theorem to determine if the temperature gradient favors weak layer formation. Is there a risk of avalanche at this location?
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