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Let's discuss a beautiful problem useful for Physics Olympiad based on Vector Analysis. Vector Analysis Problem: Let (\vec{a}=6\vec{i}-3\vec{j}-6\vec{k}) and (\vec{d}=\vec{i}+\vec{j}+\vec{k}). Suppose that (\vec{a}=\vec{b}+\vec{c}) where (\vec{b}) is parallel to (\vec{d}) and (\vec{c}) is perpendicular to (\vec{d}). Then (\vec{c}) is (A)(5\vec{i}-4\vec{j}-\vec{k}) (B)   ( 7\vec{i}-2\vec{j}-5\vec{k}) (C)    (4\vec{i}-5\vec{j}+\vec{k}) (D)    (3\vec{i}+6\vec{j}-9\vec{k}) Discussion: In the given problem, (\vec{a})=(6\vec{i}-3\vec{j}-6\vec{k}) $$\vec{d}=\vec{i}+\vec{j}+\vec{k}$$ and $$\vec{a}=\vec{b}+\vec{c}...(i)$$ […]

Let's discuss a beautiful problem useful for Physics Olympiad based on Suitcase Falling from an Airplane. The Problem: Suitcase Falling from an Airplane An airplane is flying with a velocity of \(90m/s\) at an angle of \(23^\circ\) above the horizontal. When the plane is \(114m\) directly above a dog that is standing on level ground, […]

Let's discuss a beautiful problem useful for Physics Olympiad based on Mass supported by a Hollow Cylinder. The Problem:  A mass m is supported by a massless string wound on a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass […]

A boy is standing on top of a tower of height 85m and throws a ball in the vertically upward direction with a certain speed. If 5.25 secs later he hears the ball hitting the ground, then the speed with which the boy threw the ball is ( take g=910m/s2, speed of sound in air=340m/s) […]

Let's discuss a beautiful problem useful for Physics Olympiad based on masses over a frictionless pulley. The Problem: Masses over a frictionless pulley Two bodies A and B hanging in the air are tied to the ends of a string which passes over a frictionless pulley. The masses of the string and the pulley are […]

A soldier carrying a gun with parachute A soldier with a machine gun, falling from an airplane gets detached from his parachute. He is able to resist the downward acceleration if he shoots 40 bullets a second at the speed of 500m/s. If the weight of a bullet is 49gm, what is the weight of […]

A pen of mass 'm' is lying on a piece of paper of mass M placed on a rough table. If the cofficient of friction between the pen and paper and, the paper and the table are (\mu_1) and (\mu_2) respectively, what is the minimum horizontal force with which the paper has to be pulled […]

Notes in Mathematics A Cheenta Newsletter I hope you are doing well.    First, let me congratulate all students from India and abroad who did exceptionally well in contests like I.S.I. and C.M.I. Entrance, Math Olympiads, and other science olympiads. Among our students, Aniruddha, Sambudda, and Mary deserve a special mention.    Today I wish […]

Let's discuss a beautiful problem useful for Physics Olympiad based on Particle Motion. The Problem: Particle Motion A particle Q is moving +Y axis. Another particle P is moving in XY plane along a straight line x=-d (d>0) with a uniform speed v parallel to that of Q. At time t=0, particles P and Q […]

Let's discuss a beautiful problem useful for Physics Olympiad based on Angle between Force and Momentum. The Problem: Angle between Force and Momentum A particle moves in the X-Y plane under the influence of a force such that its linear momentum p(t)=A[icos(kt)-jsin(kt)] where A and k are constants. Find the angle between the force and […]