Knowing that, ignoring air resistance, an apple falling from a height h hits the ground when2ht =If you include air resistance, then vs 0 willappear and the equation of motion becomes:dvm = -mg + kv² v(0) = 0dtWith k> 0. Show thatmggkv(t) = -tanhmand also show that the apple takes time to touch the ground iskh2khe mkgCheck that this matches the answer when we don't consider theair resistance with k → 0. Tip: for very small x valuesex 1+x and In1 + x )= x

You have asked a multipart question. Here t= time V = velocity h = height of apple from ground

Tesistal 2h If you include air resistance, then vs0 will appear and the equation dv m –mg + kv² v(0) = 0 dt With k>0. Show that v(t) = mg -tanh m and also show that the apple takes time to touch the ground is kh 2kh t = In kg Cho don't

Tesistal 2h If you include air resistance, then vs0 will appear and the equation dv m –mg + kv² v(0) = 0 dt With k>0. Show that v(t) = mg -tanh m and also show that the apple takes time to touch the ground is kh 2kh t = In kg Cho don't

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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Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the shearing and machining process, the material does not undergo up to a failure point as indicated in the stress-strain curve. Hence, the stresses induced during the forming process are greater than yield strength but less than the failure strength of the material. The process does not lead to the loss of material, so it can be said to be an economical process. During forming, the material is subjected to tensile forces, compressive forces, bending, and shearing loading conditions. The material should possess the property of ductility to undergo the forming process.

Question

Knowing that, ignoring air resistance, an apple falling from a height h hits the ground when
2h
t =
If you include air resistance, then vs 0 willappear and the equation of motion becomes:
dv
m = -mg + kv² v(0) = 0
dt
With k> 0. Show that
mg
gk
v(t) = -
tanh
m
and also show that the apple takes time to touch the ground is
kh
2kh
e m
kg
Check that this matches the answer when we don't consider the
air resistance with k → 0. Tip: for very small x values
ex 1+x and In1 + x )= x

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