Problem 12E
In rock blasting, the peak particle velocity (PPV) depends both on the distance from the blast and on the amount of charge. The article “Prediction of Particle Velocity Caused by Blasting for an Infrastructure Excavation Covering Granite Bedrock” (A. Kahriman. Mineral Resources Engineering, 2001:205218) presents data on PPV. scaled distance (which is equal to the distance divided by the square root of the charge), and the amount of charge. The following table presents the values of PPV, scaled distance, and amount of charge for 15 blasts. (Some of these data were presented in Exercise 4 in Section 7.4.)

Scaled Distance 
Amount of 
PPV (mm/s) 
(m/kg05) 
Charge (kg) 
1.4 
47.33 
4.2 
15.7 
9.6 
92.0 
2.54 
15.8 
40.0 
1.14 
24.3 
48.7 
0.889 
23.0 
95.7 
1.65 
12.7 
67.7 
1.4 
39.3 
13.0 
26.8 
8.0 
70.0 
1.02 
29.94 
13.5 
4.57 
10.9 
41.0 
6.6 
8.63 
108.8 
1.02 
28.64 
27.43 
3.94 
18.21 
59.1 
1.4 
33.0 
11.5 
1.4 
34.0 
175.0 
a. Fit the model In PPV = β0 + β1 In Scaled Distance + β2 In Charge + ε. Compute the P  value for testing H0: β1 = 0 for β0, β1, and β2.
b. The article claims that the model In PPV = β0 + β1In Scaled Distance + ε is appropriate. Fit this model. Compute the Pvalue for testing H0: fa = 0 for fa, fa. and fa.
c. Which model do you prefer? Why?
1 Charge & Coulomb's Law Charge Is a property of matter. There are two kinds of charge, positive “+” and negative “−”.1 1. An object can have positive charge, negative charge, or no charge at all. A particle which has charge causes a forceperchargeofwouldbevictim vector to exist at each point in the region of space around itself. The infinite set of forceperchargeofwouldbevictim vectors is called a vector field. Any charged particle that finds itself in the region of space where the force perchargeofwouldbevictim vector field exists will have a force exerted upon it by the forceperchargeofwouldbevictim field. The forcepercharge ofwouldbevictim field is called the electric field. The charged particle causi