A Child throws a ball straight upwards to his friend who is sitting in a tree 18 ft above ground level. a. If the ball leaves the child s hand at a height of 2 ft with an initial speed of 40 ft/sec, write a function representing the vertical position of the ball s t in ft in terms of the time t after the ball leaves the child’s hand. b. Determine the tine interval for which the ball will be more than 18 ft high.
A Child throws a ball straight upwards to his friend who is sitting in a tree 18 ft above ground level. a. If the ball leaves the child s hand at a height of 2 ft with an initial speed of 40 ft/sec, write a function representing the vertical position of the ball s t in ft in terms of the time t after the ball leaves the child’s hand. b. Determine the tine interval for which the ball will be more than 18 ft high.
Solution Summary: The author explains the function representing the vertical position of the ball s(t) in terms of time after it leaves the child’s hand.
A Child throws a ball straight upwards to his friend who is sitting in a tree 18 ft above ground level.
a. If the ball leaves the child s hand at a height of 2 ft with an initial speed of 40 ft/sec, write a function representing the vertical position of the ball
s
t
in ft
in terms of the time t after the ball leaves the child’s hand.
b. Determine the tine interval for which the ball will be more than 18 ft high.
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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