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Chapter 7: Q. 79 (page 465)
In Problems 57鈥� 80, solve each equation on the interval
The given equation has no real solution.
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Projectile Motion The horizontal distance that a projectile will
travel in the air (ignoring air resistance) is given by the equation
where is the initial velocity of the projectile, is the angle
of elevation, and g is acceleration due to gravity (9.8 meters
per second squared).
(a) If you can throw a baseball with an initial speed of 34.8 meters per second, at what angle of elevation should you direct the throw so that the ball travels a distance of 107 meters before striking the ground?
(b) Determine the maximum distance that you can throw the ball.
(c) Graph with meters per second.
(d) Verify the results obtained in parts (a) and (b) using a graphing utility.
Projectile Motion The range R of a projectile propelled downward from the top of an inclined plane at an angle to the inclined plane is given by
where is the initial velocity of the projectile, is the angle the plane makes with respect to the horizontal, and g is the acceleration due to gravity.
(a) Show that for fixed and the maximum range down the incline is given by
(b) Determine the maximum range if the projectile has an initial velocity of meters/second, the angle of the plane is , and meters/second2.
Suppose that f and g are two functions with the same domain. If for every x in the domain, the equation is called a(n) ____. Otherwise, it is called a(n) _____ equation.
Constructing a Rain Gutter A rain gutter is to be constructed of aluminum sheets inches wide. After marking off a length of inches from each edge, this length is bent up at an angle . See the illustration. The area of the opening as a function of is given by
(a) In calculus, you will be asked to find the angle that maximizes by solving the equation
Solve this equation for
(b)What is the maximum area of the opening?
(c)Graph , and find the angle that maximizes the area . Also find the maximum area. Compare the results to the answer found earlier.
Rewrite in terms of sine and cosine functions:
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