Yellowstone National Park is home to many geysers which send

Yellowstone National Park is home to many geysers, which send jets of hot water and steam into the air. Some of these geysers are listed below, with observations of height achieved, time for water to reach the and the velocity of the water leaving the ground. Considering problems 32-34 on your original Exam 1 as well as what you have learned about quadratic functions, complete the remaining problems: Complete the table. Does it take twice as much initial velocity to propel the water twice as high? Discuss how height and initial velocity are related using degree specific exam as well as reasoning from algebraic formula(s). samples from your table

Solution

In all questions we assume acc. due to gravity . g = 32ft/sec^2

formulas use : u^2 = 2gh ; h = gt^2/2

32 ) Old faithful : h = 180 ft ; t= 3.35 sec

formula: u= sqrt(2gh) = sqrt(2*32*180) = 107.33 ft/sec

Castle Geyser : t= 2.37 sec ; u= 75.84 ft/sec

h = u^2/2g = 75.84^2/2*32 = 89.87 = 90 ft

Steam boat Geyser: u= 138.56 ft/sec

h = u^2/2g = 138.56^2/(2*32) = 300 ft

Grotto Geyser : h= 10 ft ; t=0.79 sec ;

u= sqrt(2gh) = sqrt(2*10*0.79) = 3.97 ft/sec

Giantess Geyser : h = 160 ft ; u = 101.20 ft/sec

t = sqrt(2h/g) = sqrt(2*160/32) = 3.16 sec

33) u^2 = 2gh

h2 =2h1;

u2^2/u1^2 = h2/h1 = 2

u2 = u1sqrt2

It takes square root 2 times the intial velocity to propel water twice as high.