The parametric equations that model the path of the shell as a function of time t (in sec) given that after launch, an artillery specialist fires a shell from 1 m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16 ° from the horizontal. Choose a coordinate system with the origin at ground level directly below the launch position.
The parametric equations that model the path of the shell as a function of time t (in sec) given that after launch, an artillery specialist fires a shell from 1 m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16 ° from the horizontal. Choose a coordinate system with the origin at ground level directly below the launch position.
Solution Summary: The author describes the parametric equations that model the path of the shell as a function of time t (in sec).
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.
Chapter 10.6, Problem 51PE
(a)
To determine
The parametric equations that model the path of the shell as a function of time t (in sec) given that after launch, an artillery specialist fires a shell from 1m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal. Choose a coordinate system with the origin at ground level directly below the launch position.
(b)
To determine
To calculate : The time required for the shell to hit the ground if an artillery specialist fires a shell from 1m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal.
(c)
To determine
To calculate : The horizontal distance that the shell travels before it hits the ground if an artillery specialist fires a shell from 1m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal.
(d)
To determine
To calculate : The time when shell is maximum height if an artillery specialist fires a shell from 1m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal.
(e)
To determine
To calculate : The maximum height if an artillery specialist fires a shell from 1m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal.
2. Symmetry Evaluate the following integrals using symmetry argu-
ments. Let R = {(x, y): -a ≤ x ≤ a, −b ≤ y ≤ b}, where a
and b are positive real numbers.
a.
SS
Sf xye
xye¯(x² + y²)
dA
R
b.
C
sin (x − y)
-
dA
x² + y² + 1
R
Choose a convenient order When converted to an iterated integral, the following double integrals are easier to evaluate in one order
please show all steps
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