Another ex2 question help pls (1 Viewer)

[=)(=]

A particle of mass m is projected vertically upwards and experiences a resistance of magnitude mkv^2 newtons. During its downward motion, the terminal velocity of the particle is V m/s. Find the position of the particle below its maximum height when it reaches 50% of its terminal velocity.

 

[5uckerberg]

Okay, this question. Firstly we are going to have to do this step.

Find the height H okay, done by integration with that replaces the acceleration and use the boundaries of at v=u when x=0, v=0 when x=H. You should have something like this

Step 2 knowing H we will do this and terminal velocity is when acceleration=0. There will have .

Step 3, do the integral again but this time with

 

[=)(=]

ohh i had no idea i had to use definite integrals

 

[5uckerberg]

ohh i had no idea i had to use definite integrals

I mean if you want to use indefinite integrals, that is fine but I think I got this habit from doing too many Steve Howard's mechanics questions. To me, it just feels easier no need to write the +C and then works out the other things.

 

[ExtremelyBoredUser]

ohh i had no idea i had to use definite integrals

In most instances I feel its easier to just use indefinite integrals and sub in the boundaries for simplicity, maybe out of practice/routine but at times its more easier to use definite integrals for such questions. Its good to know how to use both of them for the instance you get such a question but most of the times it doesn't matter which one you do.

 

[CM_Tutor]

The indefinite integral forms can hep to avoid needing to deal with improper integrals, too.

 

[ExtremelyBoredUser]

The indefinite integral forms can hep to avoid needing to deal with improper integrals, too.

Apparently improper integrals are outside the syllabus but I've seen a lot of textbooks still incorporate them? I'm a bit confused on that aspect but I assume you can rewrite them to forms inside the syllabus so it can be assessed?

Like

is the same as


A bit confused when it comes to the technicalities.

 

[CM_Tutor]

Assuming is defined on , then yes,

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