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
23. Network Analysis The figure shows the flow of traffic
(in vehicles per hour) through a network of streets.
200
100-
-100
200
(a) Solve this system for i = 1, 2, 3, 4.
(b) Find the traffic flow when x = 0.
(c) Find the traffic flow when x = 100.
(d) Find the traffic flow when x, = 2x₂.
2\int_{-3/2}^{3/2} \sqrt{4u^2+2} du
2. Consider the following:
Prove that x, x2, and 1/x are the solutions to the homogeneous equation
corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4.
b. use variation of parameters to find a particular solution and complete the general
solution to the differential equation. I am interested in process. You may use a
computer for integration, finding determinants and doing Kramer's.
University Calculus: Early Transcendentals (4th Edition)
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