Yellow stone National Park is home to many geysers which sen

Yellow stone National Park is home to many geysers. which send jets of hot water and steam into the air. Some of these geysers ore listed below, with observations of height achieved, time water to reach the peak, 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 specific examples from your table as well as reasoning from algebraic formula(s).

Solution

Yes, it will take twice as much initial velocity to propel the water twice as high.

This is because we know that the formula for velocity = height / time.

Which means if time is constant then Velocity is directly proportional to Height.

Therefore, if height is twice then velocity will also be high.

V = H / T

Take example of Old faithful where Height and Time was given and we had to find Velocity.

Therefore, Velocity = H/ T = 180 / 3.35 = 53.73 feet per second

Now, if we say that Time is constant and Height is doubled now i.e. 2*180 = 360 feet.

Then, Velocity will also be doubled i.e. 2*53.73 = 107.46 feet per second.