Concept explainers
(a)
To calculate: The length of the path traveled by the projectile.
(a)
Answer to Problem 53E
The required length of the path traveled by the projectile is 461.749 feet.
Explanation of Solution
Given information:
The parametric equations:
The angle:
The initial velocity:
Calculation:
The given parametric equations are
Differentiate the parametric equations with respect to t .
At t = 0;
Substitute 0 for y in the expression
Thus,
And,
Consider that L be the length of the parametric curve.
So,
Write the length of the path traveled by the projectile as:
Also,
The maximum height at
Now, substitute
Hence, the required length of the path traveled by the projectile is 461.749 feet.
(b)
To calculate: The maximum height of the projectile.
(b)
Answer to Problem 53E
The required maximum height of the projectile is 41.125 feet.
Explanation of Solution
Given information:
The parametric equations:
The angle:
The initial velocity:
Calculation:
The given parametric equations are
Differentiate the parametric equations with respect to t .
At t = 0;
Substitute 0 for y in the expression
Thus,
And,
Consider that L be the length of the parametric curve.
So,
Write the length of the path traveled by the projectile as:
Also,
The maximum height at
Substitute
Hence, the required maximum height of the projectile is 41.125 feet.
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
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