Concept explainers
If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after t seconds is given by H = 10t – 1.86t2.
(a) Find the velocity of the rock after one second.
(b) Find the velocity of the rock when t = a.
(c) When will the rock hit the surface?
(d) With what velocity will the rock hit the surface?
(a)
To find: The velocity of the rock after one second.
Answer to Problem 14E
The velocity of the rock after one second is 6.28 m/s.
Explanation of Solution
Given:
The height (in meters) of the rock after t seconds is
The position function of the rock is,
Formula used:
The derivative
Zero productivity rule: “If
Calculation:
Obtain the velocity of the rock after one second.
Take the position function
Simplify further and obtain the velocity as follows.
Cancel the common term h from both the numerator and the denominator,
Thus, the velocity of the rock at time
(b)
To find: The velocity of the rock when
Answer to Problem 14E
The velocity of the rock when
Explanation of Solution
Calculation:
Obtain the velocity of the rock when
Take the position function
Simplify further and obtain the velocity as follows.
Cancel the common term h of both the numerator and denominator,
Thus, the velocity of the rock at time
(c)
To find: Obtain the time t when the rock hit the surface.
Answer to Problem 14E
The rock will hit the surface when time
Explanation of Solution
The rock will hit the surface when height of the rock is zero.
Use the zero productivity rule to take
Let
Isolate t as shown below.
Thus, the rock will hit the surface when time
(d)
To find: The velocity of the rock to hit the surface.
Answer to Problem 14E
The velocity of the rock to hit the surface is
Explanation of Solution
The rock will hit the surface when time
Substitute
Thus, the velocity of the rock to hit the surface is
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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