Concept explainers
The acceleration due to gravity at an altitude y above the surface of the earth can be expressed as
where a and y are expressed in ft/s2 and feet, respectively. Using this expression, compute the height reached by a projectile fired vertically upward from the surface of the earth if its initial velocity is (a) 1800 ft/s, (b) 3000 ft/s, (c) 36,700 ft/s.
Fig. P11.29
(a)
The height
Answer to Problem 11.29P
The height
Explanation of Solution
Given information:
The acceleration (a) due to gravity at an altitude y above the surface of the earth is
The initial velocity
Calculation:
Write the relation for the speed (a) as given below:
Here, a is the acceleration and y is the altitude.
Express acceleration (a) by differentiation velocity (v) with respective to altitude (y):
Substitute
Apply integration.
Integrate the equation.
Solve for
Calculate the height
Substitute
Therefore, the height
(b)
The height
Answer to Problem 11.29P
The height
Explanation of Solution
Given information:
The acceleration (a) due to gravity at an altitude y above the surface of the earth is
The initial velocity
Calculation:
Calculate the height
Substitute
Therefore, the height
(c)
The height
Answer to Problem 11.29P
The height
Explanation of Solution
Given information:
The acceleration (a) due to gravity at an altitude y above the surface of the earth is
The initial velocity
Calculation:
Calculate the height
Substitute
The above solution is invalid because the velocity does not reduce to zero. The velocity (v)
Therefore, the height
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Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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