A team of jubliant engineering students, celebrating winning a designcompetition, fires their potato gun straight up into the air. (a) Assuming a quadratic airdrag on the potato with magnitude F (v) = mkv^2, and taking +y to be the upward direction,show that the potato speed varies with height above the ground according to the equations: v² (y)Ae9k-2ky 9k-UfBe2ky(upward)(downward)where A and B are constants of integration. [Hint: It might be helpful to make the samechain rule substitution for i used in an earlier problem set.] (b) Using your result frompart (a), show that the potato returns to hit the not-so-jubilant-anymore engineers with afinal speedVoV∞/v² + v²where vo is the potato's initial speed, and voo := √g/k is the potato's terminal speed in air.

The forces acting on the potato when it is moving upwards are:Gravitational force:Fg = mgDrag force…

Answered: A team of jubliant engineering…

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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A team of jubliant engineering students, celebrating winning a design
competition, fires their potato gun straight up into the air. (a) Assuming a quadratic air
drag on the potato with magnitude F (v) = mkv^2, and taking +y to be the upward direction,
show that the potato speed varies with height above the ground according to the equations:

v² (y)
Ae
9
k
-2ky 9
k
-
Uf
Be2ky
(upward)
(downward)
where A and B are constants of integration. [Hint: It might be helpful to make the same
chain rule substitution for i used in an earlier problem set.] (b) Using your result from
part (a), show that the potato returns to hit the not-so-jubilant-anymore engineers with a
final speed
VoV∞
/v² + v²
where vo is the potato's initial speed, and voo := √g/k is the potato's terminal speed in air.

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