The height of a projected object on the moon is approximated by the function: S(t) = -2.7t2 + Vot + So, where S(t) is the height in feet of an object projected directly upward, with an initial velocity of vo feet per second, a starting height of so feet, and t is the number of seconds after the object is projected. In this example, an astronaut on the moon throws a baseball upward. The astronaut is 6'6" = 6.5' tall and the initial velocity of the ball is 30 feet per second, so that s(t) = -2.7t2 + 30t + 6.5. Answer the following questions (a-c) about the ball thrown on the moon. Give your answers in complete sentences including units of measure, SHOW YOUR WORK, and draw a comprehensive graph of the rocket's path, labelling the x-and y-axes, as well as all of the relevant points on your graph. a) After how many seconds is the ball 12 feet above the moon's surface? (HINT: There are two se points. Determine these points GRAPHICALLY, by graphing the appropriate functions and finding the intersection points on your calculator (Press 2nd CALC 5 (intersect), give it the left bound and the right bound, and press Enter). What are the points? Label the x,y coordinates of these points on a comprehensive graph below). R=-2.7 2.7t t = 30I TE30]?-4(2.7X5-S) t=30t J840.b 30t t6-5 -36€+5.5 5.4 t= 10.9246 O. 1865 ACT-7) b) How many seconds after it is thrown will the ball return to the moon's surface? Determine these points GRAPHICALLY, by finding the ZERO on your calculator (Press 2nd CALC 2 (zero), give it the left bound and the right bound, and press Enter). What is the point? Label the x,y coordinates of this point on your comprehensive graph below). 6- --74 +30¢ +6.5 2.7¢-36t-6.5=0 t = 30t JC-30 -4 c2.7)(-65) %3D t= 11.3?37 %3D © Schmitz 20 22:7) t= -0.2176 Unit 2: Polynomial, Rational, Power and Root Fuheti c) The ball will never reach a height of 100 feet. How can this be determined ANALYTICALLY? SHOW YOUR WORK and give your answer in a complete sentence. i60 =-2.7 + 30€ +6.5 36t 2.7t -304 + 93.5=0 5.4 tz imngtoany no. 2-27 ixorggs noom d) GRAPHICAL SOLUTION CILECA DMSLg (Draw a comprehensive graph of the functions from parts a-c above, labelling the x-y axis and the x,y coordinates of all of the relevant points from those problems):
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
Question D, The graph
![The height of a projected object on the moon is approximated by the function:
S(t) = -2.7t2 + Vot + So, where
S(t) is the height in feet of an object projected directly upward,
with an initial velocity of vo feet per second,
a starting height of so feet, and
t is the number of seconds after the object is projected.
In this example, an astronaut on the moon throws a baseball upward. The astronaut is 6'6" = 6.5' tall
and the initial velocity of the ball is 30 feet per second, so that s(t) = -2.7t2 + 30t + 6.5.
Answer the following questions (a-c) about the ball thrown on the moon. Give your answers in complete
sentences including units of measure, SHOW YOUR WORK, and draw a comprehensive graph of the
rocket's path, labelling the x-and y-axes, as well as all of the relevant points on your graph.
a) After how many seconds is the ball 12 feet above the moon's surface? (HINT: There are two se
points. Determine these points GRAPHICALLY, by graphing the appropriate functions and finding the
intersection points on your calculator (Press 2nd CALC 5 (intersect), give it the left bound and the
right bound, and press Enter). What are the points? Label the x,y coordinates of these points on a
comprehensive graph below).
R=-2.7
2.7t
t = 30I TE30]?-4(2.7X5-S)
t=30t J840.b
30t t6-5
-36€+5.5
5.4
t= 10.9246
O. 1865
ACT-7)
b) How many seconds after it is thrown will the ball return to the moon's surface?
Determine these points GRAPHICALLY, by finding the ZERO on your calculator (Press 2nd CALC 2
(zero), give it the left bound and the right bound, and press Enter). What is the point? Label the x,y
coordinates of this point on your comprehensive graph below).
6- --74 +30¢ +6.5
2.7¢-36t-6.5=0
t = 30t JC-30 -4 c2.7)(-65)
%3D
t= 11.3?37
%3D
© Schmitz 20
22:7)
t= -0.2176](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe61b3e85-d4b1-4a4a-a42a-b5d52d0e6e2f%2Fc01f5726-d3b5-47ac-80f7-48cd97b39a34%2F7o3yhk.png&w=3840&q=75)
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