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Cool goIITian

Joined:	4 Jun 2007
Post:	44

11 Aug 2007 10:19:45 IST

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568

PLEASE.......CAN SOMEONE SOLVE THIS???

None

a railway train is moving on alevel track @ 28 m.p.h

when apistolshot travellring horizontally,strikes it.the shots velocity makes an angle of 37degrees with the direction of train.the shot enters a compartment and travels along the diagonal of the ceiling.it enters at a corner farthest from the engine.the compartment being 8ft wide (perpendicular to the track),6 ft long (along the track),show that the shot is moving @ 80 m.p.h and traverses the carriage in 5/44th of a second

[IIT KHARAGPUR,1958]

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Comments (5)

Jatin Sharma

Blazing goIITian

Joined: 20 Jun 2007

Posts: 323

11 Aug 2007 10:26:37 IST

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Simple relative velocity question...

Bring the train to rest, the question's a piece of cake then....

P.S. : A question must b solved by its concept and not thot about by its origin....

pushkar limaye

Cool goIITian

Joined: 4 Jun 2007

Posts: 44

11 Aug 2007 10:28:56 IST

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JATIN,BUT HOW CAN U JUDGE THE VELOCITY OF BULLET IN THE F.O.R OF THE TRAIN???

pushkar limaye

Cool goIITian

Joined: 4 Jun 2007

Posts: 44

11 Aug 2007 10:29:36 IST

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PLS. CAN U GIVE ME A BETTER HINT???

Jatin Sharma

Blazing goIITian

Joined: 20 Jun 2007

Posts: 323

11 Aug 2007 10:36:26 IST

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Treat velocity as a vector na....

The component of velocity of the bullet perpendicular to the train remains the same nd the component along the train will be

velocity along train - velocity of the train.

I hope dis will make things simpler.......

Soumen Goswami

Forum Expert

Joined: 10 Apr 2007

Posts: 1777

19 Aug 2007 20:15:42 IST

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Let the velocity of the shot be v. This vector makes 37 with the direcion of motion of the train. Let the velocity of the train be V.
v = v(cos37 i + sin 37 j) = (v/5)(4 i + 3 j)
V = V i
where V = 28 mph
Velocity of the bullet relative to the train
U = v - V = (4v/5 - V) i + 3v/5 j
As the shot reaches the opposite corner of the ceiling, the time taken for this motion is
8/(3v/5) = 6/(4v/5 - V)
v = 80 mph, on putting V = 28 mph
Time taken = (8 x (3600/5280))/(3v/5) = 5/44 sec
The 8 ft has been converted to miles and hr to sec by multiplying by (3600/5280)

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