I E Irodov problem 1.17 | I E Irodov solution | IE Irodov physics I Application of Derivative

I E Irodov problem no 1.17
PROBLEM:1.17

From point A located on a highway (Fig. 1.2) one has to get by car as soon as possible to point B located in the field at a distance I from the highway. It is known that the car moves in the field times slower than on the highway. At what distance from point D one must turn off the highway?

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[aryansarangi]

Made question easy with diagram and simple explanation

[_.Infinity._]

This can easily be solved using Snell's law too because light also takes the shortest and fastest path possible. Drop a normal on c. Then the angle of incidence is (pi)/2 and let the angle of refraction be r. By snells law, we know sin(i)/sin(r) is constant(here the constant is eta as it is the factor by which the velocities vary)

sin(pi/2)/sin(r)= v(eta)/v
=> 1/sin(r)=eta.
=> sin(r)=1/eta---(1)
Now notice the angle adjacent to DB is also r.
Hence sin(r)=x/sqrt(x^2+l^2)---(2)
from (1) and(2)
1/eta=x/sqrt(x^2+l^2)
upon simplifying we get,
x=l/sqrt(eta^2-1)
This is a much faster approach to the problem.

[SagarKumar-evwj]

Well explained sir.. Your way of explanation is simply awesome.

[xavier]

I met a kid outside the mall crying, he had lost his 200$, so I gave him 40$ from the 200$ I found. When god blesses you, you must bless others

[karanbansal]

All chapters of irodov will be covered in this channel only ?? Plz tell bhaiya