Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical and opposite g, the ground is horizontal, and only the gravitational force acts on the object unless otherwise stated. a. Find the velocity and position vectors , for t ≥ 0. b. Make a sketch of the trajectory. c. Determine the time of flight and range of the object. d. Determine the maximum height of the object. 48. A golf ball is hit east down a fairway with an initial velocity of 〈50, 0, 30〉 m/s. A crosswind blowing to the south produces an acceleration of the ball of −0.8 m/s 2 .
Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical and opposite g, the ground is horizontal, and only the gravitational force acts on the object unless otherwise stated. a. Find the velocity and position vectors , for t ≥ 0. b. Make a sketch of the trajectory. c. Determine the time of flight and range of the object. d. Determine the maximum height of the object. 48. A golf ball is hit east down a fairway with an initial velocity of 〈50, 0, 30〉 m/s. A crosswind blowing to the south produces an acceleration of the ball of −0.8 m/s 2 .
Three-dimensional motionConsider the motion of the following objects. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical and opposite g, the ground is horizontal, and only the gravitational force acts on the object unless otherwise stated.
a.Find the velocity and position vectors, for t ≥ 0.
b.Make a sketch of the trajectory.
c.Determine the time of flight and range of the object.
d.Determine the maximum height of the object.
48. A golf ball is hit east down a fairway with an initial velocity of 〈50, 0, 30〉 m/s. A crosswind blowing to the south produces an acceleration of the ball of −0.8 m/s2.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
2. (5 points) Let f(x) =
=
-
-
- x² − 3x+7. Find the local minimum and maximum point(s)
of f(x), and write them in the form (a, b), specifying whether each point is a minimum
or maximum. Coordinates should be kept in fractions.
Additionally, provide in your answer if f(x) has an absolute minimum or maximum
over its entire domain with their corresponding values. Otherwise, state that there is no
absolute maximum or minimum. As a reminder, ∞ and -∞ are not considered absolute
maxima and minima respectively.
Let h(x, y, z)
=
—
In (x) — z
y7-4z
-
y4
+ 3x²z — e²xy ln(z) + 10y²z.
(a) Holding all other variables constant, take the partial derivative of h(x, y, z) with
respect to x, 2 h(x, y, z).
მ
(b) Holding all other variables constant, take the partial derivative of h(x, y, z) with
respect to y, 2 h(x, y, z).
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