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
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
University Calculus: Early Transcendentals (4th Edition)
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