Projectile Motion The horizontal distance that a projectile will travel in the air (ignoring air resistance) is given by the equation R ( θ ) = v 0 2 sin ( 2 θ ) g where v 0 is the initial velocity of the projectile, θ 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 θ 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 R = R ( θ ) , with v 0 = 34.8 meters per second. d. Verify the results obtained in parts (a) and (b) using a graphing utility.
Projectile Motion The horizontal distance that a projectile will travel in the air (ignoring air resistance) is given by the equation R ( θ ) = v 0 2 sin ( 2 θ ) g where v 0 is the initial velocity of the projectile, θ 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 θ 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 R = R ( θ ) , with v 0 = 34.8 meters per second. d. Verify the results obtained in parts (a) and (b) using a graphing utility.
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
is acceleration due to gravity (
meters per second squared).
a. If you can throw a baseball with an initial speed of
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.
Expert Solution
To determine
To find:
a. If you can throw a baseball with an initial speed of 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?
Answer to Problem 109AYU
a.
Explanation of Solution
Given:
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 is acceleration due to gravity ( meters per second squared).
Calculation:
a.
Expert Solution
To determine
To find:
b. Determine the maximum distance that you can throw the ball.
Answer to Problem 109AYU
b. m.
Explanation of Solution
Given:
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 is acceleration due to gravity ( meters per second squared).
Calculation:
b. Maximum range .
Expert Solution
To determine
To find:
c. Graph , with meters per second.
Answer to Problem 109AYU
c.
Explanation of Solution
Given:
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 is acceleration due to gravity ( meters per second squared).
Calculation:
c.
Expert Solution
To determine
To find:
d. Verify the results obtained in parts (a) and (b) using a graphing utility.
Answer to Problem 109AYU
The results of (a) and (b) verified in (c).
Explanation of Solution
Given:
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 is acceleration due to gravity ( meters per second squared).
University Calculus: Early Transcendentals (4th Edition)
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