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23 Feb 2007 18:52:43 IST
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A particle is projected at an angle 60 degree with vertical with speed v = 20m/s. taking g = 10m/s^2 find the time after which speed of the particle remains half of its initial speed.


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Asmita Bhattacharya's Avatar

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23 Feb 2007 19:05:31 IST
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We've to find the time t when v=10 m/s
Since at t=0 v= 20m/s at an < of 60 0 with the vertical vx=10rt3 m/s ,vy=10 m/s
So v=10m/s when vy=0
0=10-gt
so t=1 second

Cool goIITian

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23 Feb 2007 19:26:51 IST
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initial speed = 20 m/s.horizontal component of this velocity = 10 m/s. final asked speed = 10m/s. this means that when speed is 10 m/s it is at max. height as vertical component of velocity =0. therfore t =1/2(time period of progectile) = 1/2 (2 u sin theta/g)=u sin theta /g = 3 seconds.
 
Asmita Bhattacharya's Avatar

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23 Feb 2007 19:35:06 IST
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Sorry i made some mistake.
For v 2 b 10 m/s let vy=a
So a^2+(10rt3)^2=(10)^2
a^2=100-300=-200
which is not possible in the real set.

Blazing goIITian

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23 Feb 2007 21:33:56 IST
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X-vel = 20cos60=10m/s  and Y-vel= 10[ 2]3 m/s
 
after time 't', say vel=10 m/s
so, we, have,  100+v^2= 100 where v= vel in y-direction
 
so, v=0 i.e 
103-gt=0   => t=1.732 sec
Truly Mittal's Avatar

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23 Feb 2007 21:35:59 IST
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An easy way:

apply conservation of energy.....initial velocity = v and assume GPE = 0 at projecting posistion.....velocity is v/2 whn hight is h....

1/2 mv^2 = mgh + 1/2 m(v/2)^2

putting the values h = 15 meter.....

initial velocity in y direction is Vy = v cos60 (or v sin30 since angle with horizontal is 30)........===>> Vy = 20 cos 60 = 10 m/s

h = ut + 1/2 gt^2

put H = 15 , u (Vy)= 10 , g=10

Solving you get t = 1 sec

Asmita Bhattacharya's Avatar

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23 Feb 2007 21:43:41 IST
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truly
 i completely agree with ur ans. Take a salute frm me. But It's a request ...........Plz pt. out where i went wrong.
Truly Mittal's Avatar

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24 Feb 2007 01:14:50 IST
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@ ashmita

I agree with ur answer in ur second post....nd thr is no mistakr conceptually....thr might b a bug in the question....evn on solving my part we get t = 1 nd -3....nd -3 is irrelevent seeing the question...

In ne case ur concept is correct

New kid on the Block

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24 Feb 2007 18:01:29 IST
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ALL ARE WRONG ONLY KGHEDRIU IS CORRECT. GOOD DUDE
Bipin Dubey's Avatar

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26 Feb 2007 09:59:25 IST
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Its initial horizontal velocity is 20cos600 = 10 m/s
Initailly total speed = 20 m/s

When the projectile becomes horizontal (its vertical velocity becomes zero), the projectile is at maximum height and its speed at this point is half of its initial speed.

Vertical velocity = 20sin600 - gt = 0

t = 20sin600/10 = 3 sec.

Best Wishes


Truly Mittal's Avatar

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26 Feb 2007 17:12:25 IST
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@ iitkgp bipin.....plz read the question again it says 60 with vertical and not with horizontal and chk ur solution again.....

@mandar5227 .....Dude jst chk the question and solve it urself b4 posting such words "ALL ARE WRONG ONLY KGHEDRIU IS CORRECT. GOOD DUDE" for neone else.....
CyBorG's Avatar

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26 Feb 2007 17:14:22 IST
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I think Truly is right.Are you going to become an expert Truly Sir?
Truly Mittal's Avatar

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26 Feb 2007 17:18:25 IST
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If you want me to, btw am toh jst passing time in my last sem helpin aspirants
CyBorG's Avatar

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26 Feb 2007 17:22:26 IST
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Yes.You are really doing a good job by helping us.So here comes a salute SIR!!!
Bipin Dubey's Avatar

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26 Feb 2007 22:52:02 IST
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Sorry @truly to create confusions.



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