A quarterback throws a football with an initial velocity of 72 ft/sec at an angle of 25 ° . The height of the ball can be modeled by h t = − 16 t 2 + 30.4 t + 5 , where h t is the height (in ft) and t is the time in seconds after release. a. Determine the time at which the ball will be at its maximum height. b. Determine the maximum height of the ball. c. Determine the amount of time required for the bail to reach the receiver's hands if the receiver catches the ball at a point 3 ft off the ground.
A quarterback throws a football with an initial velocity of 72 ft/sec at an angle of 25 ° . The height of the ball can be modeled by h t = − 16 t 2 + 30.4 t + 5 , where h t is the height (in ft) and t is the time in seconds after release. a. Determine the time at which the ball will be at its maximum height. b. Determine the maximum height of the ball. c. Determine the amount of time required for the bail to reach the receiver's hands if the receiver catches the ball at a point 3 ft off the ground.
Solution Summary: The author explains how the arc of the parabolic curve of a quadratic function, h(t), will open downwards and the vertex coordinates will provide the maximum values
A quarterback throws a football with an initial velocity of 72 ft/sec at an angle of
25
°
.
The height of the ball can be modeled by
h
t
=
−
16
t
2
+
30.4
t
+
5
, where
h
t
is the height (in ft) and
t
is the time in seconds after release.
a. Determine the time at which the ball will be at its maximum height.
b. Determine the maximum height of the ball.
c. Determine the amount of time required for the bail to reach the receiver's hands if the receiver catches the ball at a point 3 ft off the ground.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY