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where k = 0.75 is a design parameter. a. Write down a single constraint in terms of 0 that ensures that the ball hits the ground at the given value of rf.

where k = 0.75 is a design parameter. a. Write down a single constraint in terms of 0 that ensures that the ball hits the ground at the given value of rf.

Elements Of Electromagnetics
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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We want to design a ball throwing robot arm that will throw a ball with initial velocity Vo at an angle 0 to the ground plane. Assuming that the robot arm is at coordinates r = 0 the ball will hit the ground at V sin 20 where g = 9.8 is the gravitational constant. We want to ensure that the ball hits the ground at rf = 0.1730861 meters. Unfortunately, we are not free to choose the necessary Vo and 0 since the robot design constrains the speed to be a function of the angle as Vo = k(1+ cos 0) where k = 0.75 is a design parameter. a. Write down a single constraint in terms of 0 that ensures that the ball hits the ground at the given value of xf. b. Convert the solution of 0 into a root finding problem, then solve this problem by searching for 0 in the interval [0°, 40°]. c. Calculate the necessary Vo for the 0 you have found. Hint: Although the 0 range is given in degrees, perform the calculations in radians. Note that 360° = 2n radians.
Transcribed Image Text:We want to design a ball throwing robot arm that will throw a ball with initial velocity Vo at an angle 0 to the ground plane. Assuming that the robot arm is at coordinates r = 0 the ball will hit the ground at V sin 20 where g = 9.8 is the gravitational constant. We want to ensure that the ball hits the ground at rf = 0.1730861 meters. Unfortunately, we are not free to choose the necessary Vo and 0 since the robot design constrains the speed to be a function of the angle as Vo = k(1+ cos 0) where k = 0.75 is a design parameter. a. Write down a single constraint in terms of 0 that ensures that the ball hits the ground at the given value of xf. b. Convert the solution of 0 into a root finding problem, then solve this problem by searching for 0 in the interval [0°, 40°]. c. Calculate the necessary Vo for the 0 you have found. Hint: Although the 0 range is given in degrees, perform the calculations in radians. Note that 360° = 2n radians.
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