A body is on a wedge(Traingular ABC), which is right angled at B and B touches the ground. Body is at point A
A body can move from A to C by two different pathes:
- Sliding along the inclined plane AC (lenght l) without friction - or
- falling from A to B (height h), where it is directed to C (BC = b) (basically the velocity between B->C is same as velocity when the body reaches point B!)
Which will be faster?
And what will be the route that u will chose?
Difficulty Level: 3-4 (Basically u will have to use derivatives!)
1Body will slide from A to C faster.
Because from A to C gravity will act so the time taken will be equal to the time taken from A to B.! simple
So B to C will be ony extra time!
1Saurahb's answer is wrong.. bcos if the slide has very very less slope, the time to fall to B will be very small. But to travel to AC will be every large.
so there is something wrong with saurabh's explanation.
I dont know what
I cant find an answer either....
1but ur method is only oral.. nothing is numerical in it!
i mean u understand no?
1I think this is wrong solution.
AC=b
AB=c
BC=a
By pythagoras thm: a2+c2=b2
theta (θ) = angle B
Sin(θ) = c/b
If going by Path AC
acceleration along path AC = mg Sin(θ)/m =gSin(θ)
Time to reach C will be b2/{2gSin(θ)}
If going by Path A-B-C
Accleration along path AB=g.
Time to reach B = c2/2g
velocity on reaching the point C = g.t = c2/2
Time to travel BC = 2a/c2
Total time on Path A-B-C = c2/2g + 2a/c2
SO we have to compare 2 numbers
b2/{2gSin(θ)} and c2/2g + 2a/c2
b3/(2gc) and c2/2g + 2a/c2
now i am stuck.. how do i proceed !!!
1U HAVENT GIVEN ANY VALUES OF H OR RATIO OF H:L...INFORMATION IS INSUFFICIENT...
1yes bhavesh .. u are absolutely right...
This is the sole reason i had not given this value... u have to figure out how will this depend on H/L...
In the sense that it is not a one way answer... it will increase for some and decrease for other...
Lets see if you could try for H/L near 0
and L/H near 0... then what will be the solutions...
actually Ritu has a good approach.. but for obvious reasons she got stuck.!
1May be, I should have put a higher value to the Difficulty
Definitely, There is no "answer" to my problem.
1what is here when u say the body falls the height h n is directed towards c ??
so EVEN though if the velocity when it reaches the point B is similar to the velocity at C , it wud take longer coz it has to travel the hypotenus !!!
so obviously the chance for sliding body to get on earlier is possible PROVIDED the slope not tending to ZERO
other wise bro i guess no orthodox for this one !
1hmm...
i will give another hint..
what when the height is very very small?