A pyrotechnic rocket is fired from a platform 2 ft high at an angle of 60 ° from the horizontal with an initial speed of 72 ft/sec . Choose a coordinate system with the origin at ground level directly below the launch position. a. Write parametric equations that model the path of the shell as a function of the time t (in sec) after launch. b. Approximate the time required for the shell to hit the ground. Round to the nearest hundredth of a second. c. Approximate the horizontal distance that the shell travels before it hits the ground. Round to the nearest foot. d. When is the shell at its maximum height? Find the exact value and an approximation to the nearest hundredth of a second. e. Determine the maximum height.
A pyrotechnic rocket is fired from a platform 2 ft high at an angle of 60 ° from the horizontal with an initial speed of 72 ft/sec . Choose a coordinate system with the origin at ground level directly below the launch position. a. Write parametric equations that model the path of the shell as a function of the time t (in sec) after launch. b. Approximate the time required for the shell to hit the ground. Round to the nearest hundredth of a second. c. Approximate the horizontal distance that the shell travels before it hits the ground. Round to the nearest foot. d. When is the shell at its maximum height? Find the exact value and an approximation to the nearest hundredth of a second. e. Determine the maximum height.
Solution Summary: The author calculates the parametric equation that represents the path of a shell as the function of time, if the rocket is fired with an initial speed of 72ft/sec
A pyrotechnic rocket is fired from a platform
2
ft
high at an angle of
60
°
from the horizontal with an initial speed of
72
ft/sec
. Choose a coordinate system with the origin at ground level directly below the launch position.
a. Write parametric equations that model the path of the shell as a function of the time
t
(in sec) after launch.
b. Approximate the time required for the shell to hit the ground. Round to the nearest hundredth of a second.
c. Approximate the horizontal distance that the shell travels before it hits the ground. Round to the nearest foot.
d. When is the shell at its maximum height? Find the exact value and an approximation to the nearest hundredth of a second.
e. Determine the maximum height.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate of
0.35%. Use this information for all the problems below.
1. Find an exponential function f(t) that gives the population of Tattooine t years from now. (3
points)
A house was valued at $95,000 in the year 1988. The value appreciated to $170,000 by the year 2007.
A) If the value is growing exponentially, what was the annual growth rate between 1988 and 2007?
Round the growth rate to 4 decimal places.
r =
B) What is the correct answer to part A written in percentage form?
r = 3
%.
University Calculus: Early Transcendentals (4th Edition)
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