Math 112 Calculus
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A spacecraft moves along a path described by the parametric equations shown below for the first 200
s after launch. Here, x and y are measured in meters, and t is measured in seconds. Find the magnitude and direction of the velocity of the spacecraft 20.0s and 200 s after launch.
x=401+t4?1,
y=60t3/2
What would be the first step in finding the velocity of the spacecraft at a given time?
Differentiate the x- and y-position components to get the x- and y-velocity components.
Find the values of x and y for the given value of t.
Differentiate y with respect to x.
Use the fact that distance=rate×time.
Find the magnitude of the velocity of the spacecraft when t=20.0
s.
The magnitude is approximately nothing
m/s.
(Round to the nearest integer as needed.)
Find the direction of the velocity of the spacecraft when t=20.0
s. Enter an angle
?
such that
0°??<360°.
The direction is approximately nothing°.
(Type an integer or decimal rounded to one decimal place as needed.)
The answer is undefined.
Find the magnitude of the velocity of the spacecraft when t=200
s.
The magnitude is approximately nothing
m/s.
(Round to the nearest integer as needed.)
Find the direction of the velocity of the spacecraft when t=200
s. Enter an angle
?
such that
0°??<360°.
The direction is approximately nothing°.
(Type an integer or decimal rounded to one decimal place as needed.)
The answer is undefined.
Sketch the graph of the given function by determining the appropriate information and points from the first and second derivatives.
y=4x3?48x?3
What are the coordinates of the relative maxima?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
nothing
(Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
There is no maximum.
What are the coordinates of the relative minima?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
nothing
(Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
There is no minimum.
What are the coordinates of the points of inflection?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
nothing
(Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
There are no inflection points.
