In applications involving an object's position, s(t), the first derivative s'(t) is the object's velocity, s"(t) is the object's acceleration. The derivative of acceleration, s'"(t), is known as the object's jerk. The next three derivatives are referred to as snap, crackle, and pop. Example 8: Neglecting air resistance, the height, h, of an object thrown upward from a height of 120 feet (from the edge of a cliff let's say...) with an initial velocity of 48 feet per second is given by h(t) = -16t² + 48t 120 where t is the number of seconds after release. Note that this model is valid until the object hits the ground. (a) Find the velocity of the object as a function of t. (You may use the shorthand "rules".) (+7=-32+ 48 (b) Find the acceleration of the object as a function of t. (c) When is the object moving up? What is the maximum height of the object? When is it falling? How far does the object travel (vertically)?
In applications involving an object's position, s(t), the first derivative s'(t) is the object's velocity, s"(t) is the object's acceleration. The derivative of acceleration, s'"(t), is known as the object's jerk. The next three derivatives are referred to as snap, crackle, and pop. Example 8: Neglecting air resistance, the height, h, of an object thrown upward from a height of 120 feet (from the edge of a cliff let's say...) with an initial velocity of 48 feet per second is given by h(t) = -16t² + 48t 120 where t is the number of seconds after release. Note that this model is valid until the object hits the ground. (a) Find the velocity of the object as a function of t. (You may use the shorthand "rules".) (+7=-32+ 48 (b) Find the acceleration of the object as a function of t. (c) When is the object moving up? What is the maximum height of the object? When is it falling? How far does the object travel (vertically)?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Transcribed Image Text:In applications involving an object's position, s(t), the first derivative s'(t) is the object's velocity,
s"(t) is the object's acceleration.
The derivative of acceleration, s'"(t), is known as the object's jerk. The next three derivatives are
referred to as snap, crackle, and pop.
Example 8: Neglecting air resistance, the height, h, of an object thrown upward from a height of 120 feet
(from the edge of a cliff let's say...) with an initial velocity of 48 feet per second is given by
h(t)
-16t² +48t4 120
where t is the number of seconds after release. Note that this model is valid until the object hits the
ground.
=
(a) Find the velocity of the object as a function of t. (You may use the shorthand "rules".)
h(+1-32+ 48
(b) Find the acceleration of the object as a function of t.
(c) When is the object moving up?
What is the maximum height of the object?
p
When is it falling?
How far does the object travel (vertically)?
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