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To find:
a. The rectangular equation of the trajectory and identify the curve.
![Check Mark](/static/check-mark.png)
Answer to Problem 60AYU
a.
Explanation of Solution
Given:
The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations.
,
Formula used:
,
Calculation:
a. ,
is a quadratic function of and it represents the graph of a parabola where , and .
To find:
b. To show that the projectile hits the ground when .
![Check Mark](/static/check-mark.png)
Answer to Problem 60AYU
b.
Explanation of Solution
Given:
The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations.
,
Formula used:
,
Calculation:
b.
To find:
c. How far has the projectile traveled (horizontally) when it strikes the ground? In other words, find the range R.
![Check Mark](/static/check-mark.png)
Answer to Problem 60AYU
c.
Explanation of Solution
Given:
The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations.
,
Formula used:
,
Calculation:
c. To find R
We substitute in
To find:
d. Find the time when . Then find the horizontal distance and the vertical distance traveled by the projectile in this time. Then compute . This is the distance R, the range, that the projectile travels up a plane inclined at to the horizontal .
![Check Mark](/static/check-mark.png)
Answer to Problem 60AYU
d. as
Explanation of Solution
Given:
The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations.
,
Formula used:
,
Calculation:
d.
;
At
hence,
as
Chapter 10 Solutions
Precalculus
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
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