Concept explainers
(a)
To find: The distance of stone above the ground level.
(a)
Answer to Problem 43E
The distance of stone above ground level at time t is
Explanation of Solution
Given data:
The distance between upper observation deck and ground is 450 m.
Formula used:
Write the expression for acceleration function
Here,
Write the expression for velocity function
Here,
Antiderivative of
Calculation:
At first observation, velocity is zero and position is at 450 m at
The motion of stone is close to ground, so the motion is considered as gravitational constant
Write the expression for acceleration function
Substitute
Antiderivate the expression with respect to t,
Here,
C is arbitrary constant.
Substitute 0 for t in equations (3),
Substitute 0 for
Substitute 0 for C in equation (3),
Substitute
Antiderivate the expression with respect to t.
Here,
D is arbitrary constant.
Substitute 0 for t in equation (6),
Substitute 450 for
Substitute 450 for D in equation (6),
Thus, the distance of stone above ground level at time t is
(b)
To find: The time that stone takes to reach ground.
(b)
Answer to Problem 43E
The time that stone takes to reach ground is 9.58 seconds.
Explanation of Solution
Given data:
The distance between upper observation deck and ground is 450 m.
Calculation:
When the stone reaches the ground, the positional function reaches zero. Hence,
Substitute
Take square root on both sides.
Thus, the time that stone takes to reach ground is 9.58 seconds.
(c)
To find: The velocity that stone strikes the ground.
(c)
Answer to Problem 43E
The velocity that stone strikes the ground is
Explanation of Solution
Given data:
The distance between upper observation deck and ground is 450 m.
Calculation:
Substitute 9.58 seconds for t in equation (5),
Thus, the velocity that stone strikes the ground is
(d)
To find: The time that stone takes to reach ground.
(d)
Answer to Problem 43E
The time that stone takes to reach ground, when it is thrown downward with speed of
Explanation of Solution
Given data:
The speed is
Formula used:
Write the expression to find the roots of
Here,
a, b, and c are constants.
Calculation:
The stone is thrown downwards with a speed of
Substitute –5 for
Substitute –5 for C in equation (3),
Substitute
Antiderivate the expression with respect to t,
Here,
D is arbitrary constant.
Substitute 0 for t in equation (9),
Substitute 450 for
Substitute 450 for D in equation (9),
Substitute
Compare the expressions
Substitute 4.9 for a, 5 for b, and –450 for c in equation (8),
Hence, the two possible values of t are,
The time cannot be a negative, so the value of t is 9.09 seconds.
Thus, the time that stone takes to reach ground, when it is thrown downward with speed of
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning