Tutor profile: Shashwat K.
Subject: Physics (Waves and Optics)
Have you ever wondered why does light bend on entering a medium of a different optical density? I mean I know books usually tell us about how the change in wavelength and thus the speed of light causes it to bend, but come on, if I asked you to drive slow on a road you'd simply drive slow not start driving in a different direction. I know some books might teach you the principle of least action where light travels through a path that takes the least amount of time to reach a point but tell me honestly - are you comfortable personifying something as fundamental as light. I mean are you really willing to believe as yet that light has brains and thinks of the path of shortest time. (although you may be forced to believe that everything in the universe has some innate sense of understanding when you study quantum)
I use the Huygens wavefront theory along with a lot of diagrams to make the child understand how can we say that light would bend while obliquely entering a medium of different optical density. (without making the children assume the light has brains)
Subject: Physics (Newtonian Mechanics)
Have you ever thought about why the astronauts that visit the ISS seem to experience weightlessness although they are still in a very strong gravitational field of the earth? Or why if the Earth is being attracted towards the Sun does it not inch closer towards the sun and eventually get annihilated. If you're going to tell me that's because the gravitational pull is balanced by the centrifugal force then let me also tell you that centrifugal force is 'pseudo' force that SEEMS to be acting on a body when viewed from a non-inertial frame.
I could explain this answer to a 10-year-old child provided I get to draw a few diagrams first. For a 15-year-old child, I can add another layer of understanding coming from inertia of motion and finally children who have studied vectors and projectile motion can understand this completely working out the mechanics behind it.
A ball is thrown in the vertically upward direction from the base of a building 245 m high at a speed of 40 m/s. 2 seconds later another ball is dropped from the top of the building. Taking acceleration due to gravity as 10 m/s^2 calculate where and when will the balls cross each other.
The conventional method of solving this question would involve assuming the balls to cross each other at some height - h and at some time - t and then making two equations for these two motions keeping in mind that the second ball only moves for t-2 seconds. This procedure would result in getting two equations for two unknowns (one of which will appear as a quadratic) and then eliminating the linear unknown to get an answer that turns out to be faulty. Another method that usually teachers would recommend for this question would be to enter the frame of one of the balls and then solving the question for after how much time does one cross the other. This procedure although shorter would result in the same faulty answer obtained above. The thing to be noticed in the faulty answers is that the time of crossing each other exceeds the time of flight of the first ball. Hence the balls do not cross each other while in the air and thus the correct answer would be the time taken by the second ball to land onto the ground (obviously assuming that the first one doesn't bounce) answer - 7 seconds.
needs and Shashwat will reply soon.