A projectile fired from the point (0,0) at an angle to the positive x-axis has a trajectory given by y = Cx- (1 + C²)| HIE In this formula, x is the horizontal distance in meters, y is the height in meters, v is the initial velocity in meters per second, g=9.81 m/ sec is the acceleration due to gravity, and C>0 is a constant determined by the angle of elevation. A howitzer fires an artillery round with a velocity of 882 m/sec. Answer parts (a) and (b). (a) If the round must clear a hill 170 meters high at a distance of 2331 meters in front of the howitzer, what C values are permitted in the trajectory equation? (0.088 67 951) (Type your answer in interval notation. Round the final answer to the nearest thousandth as needed. Round all intermediate values to five decimal places as needed.) (b) If the goal in part (a) is to hit a target on the ground 71 kilometers away, is it possible to do so? If so, for what values of C? If not, what is the maximum distance the round will travel? Select the correct choice below and fill in the answer box to complete your choice. O A. No it is not possible. The maximum distance the round will travel is m. O B. Yes, it is possible for the value(s) (Use a comma to separate answers as needed. Round the final answer to the nearest thousandth as needed. Round all intermediate values to five decimal places as needed.)
A projectile fired from the point (0,0) at an angle to the positive x-axis has a trajectory given by y = Cx- (1 + C²)| HIE In this formula, x is the horizontal distance in meters, y is the height in meters, v is the initial velocity in meters per second, g=9.81 m/ sec is the acceleration due to gravity, and C>0 is a constant determined by the angle of elevation. A howitzer fires an artillery round with a velocity of 882 m/sec. Answer parts (a) and (b). (a) If the round must clear a hill 170 meters high at a distance of 2331 meters in front of the howitzer, what C values are permitted in the trajectory equation? (0.088 67 951) (Type your answer in interval notation. Round the final answer to the nearest thousandth as needed. Round all intermediate values to five decimal places as needed.) (b) If the goal in part (a) is to hit a target on the ground 71 kilometers away, is it possible to do so? If so, for what values of C? If not, what is the maximum distance the round will travel? Select the correct choice below and fill in the answer box to complete your choice. O A. No it is not possible. The maximum distance the round will travel is m. O B. Yes, it is possible for the value(s) (Use a comma to separate answers as needed. Round the final answer to the nearest thousandth as needed. Round all intermediate values to five decimal places as needed.)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A projectile fired from the point (0,0) at an angle to the positive x-axis has a trajectory given by y = Cx - (1 +c2) | :
In this formula, x is the horizontal distance in meters, y is the height in meters, v is the initial velocity in meters per second,
g = 9.81 m/ sec- is the acceleration due to gravity, and C>0 is a constant determined by the angle of elevation.
A howitzer fires an artillery round with a velocity of 882 m/sec. Answer parts (a) and (b).
(a) If the round must clear a hill 170 meters high at a distance of 2331 meters in front of the howitzer, what C values are permitted in the trajectory equation?
(0.088,67.951)
(Type your answer in interval notation. Round the final answer to the nearest thousandth as needed. Round all intermediate values to five decimal places as needed.)
(b) If the goal in part (a) is to hit a target on the ground 71 kilometers away, is it possible to do so? If so, for what values of C? If not, what is the maximum distance the round will travel? Select the correct choice below and fill in the answer box to complete your
choice.
O A. No it is not possible. The maximum distance the round will travel is
m.
O B. Yes, it is possible for the value(s)
(Use a comma to separate answers as needed. Round the final answer to the nearest thousandth as needed. Round all intermediate values to five decimal places as needed.)
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