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.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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