This section uses real world hurricane information to solve square root equations. Scratch paper and a graphing calculator are needed.

Source: Satellite image of hurricane, NASA

In a hurricane, the mean sustained wind velocity v (in meters per second) is given by

v(p) = 6.3√1013 − p  

where p is the air pressure (in millibars) at the center of the hurricane. 

1. What is the mean sustained wind velocity of a hurricane with an eye pressure of 1200 millibars?
   
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   Check Your Answer

   v(400) = 6.3√1013 − 400
   
   = 6.3√613
   
   = 156 m/s
   
   
   
2. Determine the air pressure at the center of a hurricane when the mean sustained wind velocity is 100 miles/hr (44.7 meters/sec).
   
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   Check Your Answer

   44.7 = 6.3√1013 − p
   
   7.09524 = √1013 − p
   
   50.34240 = 1013 − p
   
   p = 1013 − 50.34240
   
   p = 962.658 millibars
   
   
   
3. If the pressure at the eye of hurricane is 850 millibars and it drops 10%, does the velocity increase or decrease?  By what percent?
   
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   Check Your Answer

   First, determine the velocity when the pressure is 850 millibars:
   
   v(850) = 6.3√1013 − 850
   
   v(850) = 6.3√163
   
   
   v(850) = 80.433 m/s
   
   
   Next, determine the new pressure if the original pressure drops 10%.
   

   Pnew = 850 − .10(850)
   Pnew = 850 − 85	OR	Pnew = .9(850)
   Pnew = 765		Pnew = 765

   Now calculate the new velocity:
   
   v(765) = 6.3√1013 − 765
   
   v(765) = 6.3√248
   
   v(765) = 99.212 m/s
   
   
   
   * When the pressure dropped, the velocity increased.
   
   Finally, determine by what percent the velocity increased.
   
   % x v_old = v_new
   
   % x 80.433 = 99.212
   
   % = 99.212 80.433
   
   % = 1.233
   
   * When the pressure dropped 10%, the velocity increased by 23.3%.