Imagine a 2D space. (0,0) is where our interceptor missile is, and $y_0$ is where our target is currently moving with a velocity of $v_2$ The interceptor will come close to the target in a certain time t. Our target can travel at a constant speed of Vt and the interceptor is at a constant speed Vi. The magnitude and direction of the target won't change, but the interceptor is always following the target, such that once the missile is launched, it will hit the moving target. I wonder how I calculate the hit time t? I tried to solve an ODE but couldn't reach the solution, which should be: $$t= V ..read more

For a straight wire moving perpendicular to a uniform magnetic field in velocity v, So the induced e.m.f in the conductor as it moves through the magnetic field is: ε = BLv. However, isn't the rate of magnetic flux cut by the straight wire itself zero? The straight wire has the same amount of flux cutting through it every second. The area where the wire cut across the magnetic flux is changing with time, but it's not a closed area. Does Faraday's law apply to unclosed areas too? Also, Faraday's law states that 'the magnitude of the emf induced in a circuit is proportional to the rate of chang ..read more

A charged particle in vacuum and stable motion would induce a time-variant but non-radiating electromagnetic field, whose pattern moves at exactly the particle's speed, but in a medium with lower speed of light this solution is no longer valid, and the only legal solution becomes that of a bow shock (Cerenkov Radiation). This is analogous to supersonic flow. However even in this flow regime we have isentropic compression body, i.e. a disturbance can travel upstream at supersonic speed without causing shockwave, the air would return to original state at infinity behind the body, and none of the ..read more

Suppose two objects A and B are travelling on a smooth surface (in a linear path) with the same acceleration. B is behind A and having contact with A. Supposing the velocities of the two objects are the same in any given moment, can object B apply a force on A? My next problem is, say we have a trolley on a smooth surface. Can we keep a wooden block in vertical equilibrium, touching the outer wall of the trolley (which have friction) by balancing the weight of the block only by the frictional force excerted by the trolley wall on the block, if we are acaccelerating the trolley? So my line of t ..read more

this question is a fun challenge, and I need you to have fun with being serious while solving it and i hope it will make you wonder! btw errors could be there, so feel free the mention those in the comment ..read more

In Schwarzschild black hole the singularity is space-like. In Kerr hole it is time-like. Is there any continuous transformation between those solutions? Can Schwarzschild solution be obtained by taking Kerr solution in zero spin limit ..read more

How to project Ga onto R3 Does the orientation of an angle play an important role in vector projection ..read more

Inspired by this article, where a Texas family claim that an "Amber Alert" on their son's Airpods caused his eardrum to rupture. https://www.dailymail.co.uk/news/article-10830803/Boy-suffered-ruptured-ear-drum-hearing-loss-Apple-AirPods-blared-Amber-Alert.html According to this, sound levels starting from 165 decibels would cause eardrum rupture: When the loudness of a sound exceeds 165 dB, the pressure wave may also rupture the tympanic membrane. https://evidence.unboundmedicine.com/evidence/view/EBMG/457351/all/Acute_acoustic_trauma#:~:text=An%20intense%20sound%20wave%20will,also%20rupture ..read more

If a piece of hot metal (around 100 degrees celsius) is placed in a cup of water (around 32 degrees celsius) the metal will naturally give off heat to the water, until they reach a final temperature. However, will the metal also give off heat to the surrounding air? The air is around 20 degrees celsius ..read more

This image was shown to us to illustrate how a tornado forms due to a low pressure region (also see Jet engine vortices). I find it odd that the tornado always ends up at the ground, where it is a dead end. Why not say, it orients horizontally, where there is more air available to suck inwards ..read more