The Atmosphere: An Introduction to Meteorology (14th Edition)
The Atmosphere: An Introduction to Meteorology (14th Edition)
14th Edition
ISBN: 9780134758589
Author: Frederick K. Lutgens, Edward J. Tarbuck, Redina Herman, Dennis G. Tasa
Publisher: PEARSON
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Chapter 5, Problem 5BN
To determine

The strength of the updrafts in the storm that was necessary to support the stone just before it began to fall and convert answer from meters per second to feet per second and then to miles per hour when the record for the largest hailstone in the United States was set on July 23, 20 I 0, in Vivian, South Dakota. It was 8 inches in diameter and 18.62 inches in circumference, and it weighed nearly 2 pounds. The maximum fall speed of a spherical hailstone of diameter d can be calculated using V = k2d, where k = 20 if d is in centimeters and V is in meters per second.

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Draw a right-handed 3D Cartesian coordinate system (= x, y and z axes). Show a vector A with tail in the origin and sticking out in the positive x, y and z directions. Show the angles between A and the positive x, y and z axes, and call these angles α₁, α₂ and α3 Prove that Ax Acos α₁ Ay = Acos α₂ A₂- Acos α3
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Draw a third quadrant vector C. (remember that boldface characters represent vector quantities). Show the standard angle 0 for this vector (= angle that C makes with the positive x- axis). Also show the angle that C makes with the negative y-axis: call the latter angle 8. Finally, show the smallest angles that C makes with the positive x-axis and the positive y-axis: call these angles p1 and p2, repectively. a) Prove the following formulas for the components of C involving the standard angle (hint: start with the formulas for the components based on the angle & and then use (look up if necessary) co-function identities linking cosine and sine of 8 to sine and cosine of 0 since 8 = 3π/2-8 (this will switch cosine and sine around and eliminate - signs as well)) - C=Ccose C₁=Csine b) Prove the following formulas for the components of C: C=Ccosp1 C=Ccosp2
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