Azhagu The Super Cop
Azhagu the super cop was chasing a super thief which had special powers because of which the thief can fly but at a constant height from the ground. After too too much of runing the thief gets tired and stops, seeing this Azhagu fires a bullet with some angle from ground having max. height .The bullet should have hit the thief.
But as soon as the bullet left the gun the thief starts to run once again with a constant velocity , but still Super Cop Azhagu's bullet hit's the thief .
Then the ratio of and horizontal velocity of bullet is of the form .
Find the value of .
Note:
- Assume all the conditions to be ideal
- Azhagu is on ground and the thief is flying at every instant of time
- Bullet missed the target once.
Extra Credit :- If Azhagu is the super cop then who is the thief ???
The answer is 2.
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We can assumue t 1 and t 2 to be two instants of time for which the particle is at height h .
Substituting u ∗ sin θ = 6 ∗ g ∗ h in the equation for h we get a quadratic which gives two values of t i.e. t 1 and t 2 . Here t 2 > t 1 .
Now the distance travelled by particle is u ∗ cos θ ∗ t 2 . Which is equal to u ∗ cos θ ∗ t 1 + v ∗ t 2 . Here u ∗ c o s ( t h e t a ) ∗ t 1 is the initial horizontal distance between them.
Equating them we get ( v / u ∗ cos θ ) = 4 / ( 6 + 2 ) = 2 ∗ k / ( k + 1 ) .
Hence k = 2 / 3