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
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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Question
Urgent
Numerical method
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69a71445-2a16-4798-ba48-f74ecbdf1117%2F184fa4fd-d9e5-4b94-a23c-c17bca4ffab0%2Faus7git_processed.png&w=3840&q=75)
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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