Question

Wind Chill 50 45 40 35 30 Wind Speed (km/h) 25 20 15 10 5 0 in -10 -15 -20 35 40 -45 -50 Air Temperature (°C) Task: The wind chill index measures the sensation of cold on the human skin. In October 2001, Environment Canada introduced the wind chill index above. Each curve represents the combination of air temperature and wind speed that would produce the given wind chill value. For example, a temperature of -25°C and wind speed of 35 km/h produce a wind chill of - 40°. 1. At a wind chill of - 35, frostbite is possible after 10 min. Give two combinations of temperature and wind speed that would produce this wind chill. P3-3

Answer 1

solution- Task tere, At the wind chill Of -35, the combinations of wind speed and temperature are shown below i wind speed Air temperature : -20 is, wind speed = 5 km/h Air temperator = -30 = 50 km/h -35 and, are tere, -20°c, one could feel maximum wind chill is wind chill lines exponential relationship witte wind speed and air temperature. since coind ç air temperature both affect majority how human skin feel cold, it is reasonable calculate and get insights from exponential graph lines chill. the speed of win the graph of wind chill vs. wind speed (m/h) is shown below Figure : 4 Here, the exponential function y=c(a)x doesn't föt date when wind chill values
FIGURE:: 1
Wind chill vs. Wind speed (km/h) Wind chill 27.2e^4.82E-03x R' = 0.868 45 37 38 40 36 35 35 37 37 38 34 33 33 32 35 31 29 27 30 24 25 Wind chill 20 15 10 5 0 20 40 60 80 Wind speed (km/h)

are negative, because power exponential function always gived positive value, therefore, in order to fit the date we need to take absolute value of wind chills and exponential function Y = ccadx fit the does Wind chill wind (km/h) The range of the function is minimum and maximum wind chill values, which is from the date of VS speed 0 to 38 . Here, 'y' value represent the wind chill We in km/h and "x" value represent the wind speed Ws veluy. So, equation of exponentid graph is (4.82x103) Ws Wc = 27.2. è the calculate wind chill at different wind speeds :- wind Chiny are . here, & when wind Speed is Ws : 0 Amin : (4.82x103) x 0 from ean Wc 27.2.e 27.2 (eº)

27.2 (1) - 27. 2 when wind speed is . Ws= lootmin : 27.2 x 14.82x10+3)x100 from eano → Wc = = 27. 2 * ¢ 1-61930) 44.04 Wc = 44:04 * when wind speed is 200 Ws= kmoln (4.82x103)x200 from eam o We = 27.2 x e 27.2 x (2.62205) 71-32 IWC -71:32 5 Given equation, W = 13:12 70: 6205 x Tair 11:37 xv°.16 +0.3965x Tain x 10.16 Here above wind chill index ean 6 is indeed correct exponential function and, The wind chill indea ear 0 et 1

0:16 11.37 x vo vo 0:16 19,3 x (100)0-16 temperature Toir -20 ist 0-16 W = 13.12 + 0.6215 % (-20)-11.37 x V +0.3965 % (-20) x v0.16 = 13:12 - 12.25 7.93 x 0.87 - 19.3 x v0.16 3) To calculate wind chill at different wind speeds: *when wind speed Vs Okm/h from eano 0187 -19-3 X 0.87 when wind speed V= 100 km/ from a 0.87 (0) 0.16 W 0.87 40.3234 w - 39.45 * when wind speed V= 200 cm/s from 0.87 - 19,3 * (20090.16 = 0.87 45.0528 W =-44.18 Hence, the given model model developed E are far away match the predicted values,