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Two particles of mass m and 4m are connected by a light inelastic string of length 3a, which passes through a small smooth fixed ring. The heavier particle hangs at rest at a distance 2a beneath the ring, while the lighter particle describes a horizontal circle with constant speed. Find (a) The distance of the plane of the circle below the ring. (b) The angular speed of the lighter particle.

$$\mathrm{Two}\:\mathrm{particles}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{and}\:\mathrm{4}{m}\:\mathrm{are}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{light}\:\mathrm{inelastic} \\ $$$$\mathrm{string}\:\mathrm{of}\:\mathrm{length}\:\mathrm{3}{a},\:\mathrm{which}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{a}\:\mathrm{small}\:\mathrm{smooth}\:\mathrm{fixed}\:\mathrm{ring}. \\ $$$$\mathrm{The}\:\mathrm{heavier}\:\mathrm{particle}\:\mathrm{hangs}\:\mathrm{at}\:\mathrm{rest}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{2}{a}\:\mathrm{beneath}\:\mathrm{the}\:\mathrm{ring}, \\ $$$$\mathrm{while}\:\mathrm{the}\:\mathrm{lighter}\:\mathrm{particle}\:\mathrm{describes}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{constant} \\ $$$$\mathrm{speed}. \\ $$$$\:\mathrm{Find} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{below}\:\mathrm{the}\:\mathrm{ring}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{angular}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lighter}\:\mathrm{particle}. \\ $$

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At what speed should a basket ball player project a ball from a height of 2.1 m above the ground at an angle of 38Β° to the horizontal so that it just passes through a basket ball net which is at a horizontal distance of 5 m from the initial position of the ball and 3 m above the playground. at determine the balls maximum height above the ground.

$$\:\mathrm{At}\:\mathrm{what}\:\mathrm{speed}\:\mathrm{should}\:\mathrm{a}\:\mathrm{basket}\:\mathrm{ball}\:\mathrm{player}\:\mathrm{project}\:\mathrm{a}\:\mathrm{ball}\:\mathrm{from}\:\mathrm{a}\:\mathrm{height} \\ $$$$\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{m} \\ $$$$\mathrm{above}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{38}Β° \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{so}\:\mathrm{that}\:\mathrm{it}\:\mathrm{just}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{a}\:\mathrm{basket}\:\mathrm{ball}\:\mathrm{net}\:\mathrm{which} \\ $$$$\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{5}\:\mathrm{m}\:\mathrm{from}\:\mathrm{the}\:\mathrm{initial} \\ $$$$\mathrm{position}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{and}\:\mathrm{3}\:\mathrm{m}\:\mathrm{above}\:\mathrm{the}\:\mathrm{playground}.\:\mathrm{at}\:\mathrm{determine}\:\mathrm{the}\:\mathrm{balls} \\ $$$$\mathrm{maximum}\:\mathrm{height}\:\mathrm{above}\:\mathrm{the}\:\mathrm{ground}. \\ $$

Question Number 135558    Answers: 1   Comments: 1

A boy throws a ball at a vertical wall 4 m away. The ball is 2 m above ground when it leaves the girl's hand with initial velocity of 10√2 π‘š/𝑠 at 45ΒΊ. Horizontal component is reversed only. Where does the ball hit the ground after bounce?

$$ \\ $$A boy throws a ball at a vertical wall 4 m away. The ball is 2 m above ground when it leaves the girl's hand with initial velocity of 10√2 π‘š/𝑠 at 45ΒΊ. Horizontal component is reversed only. Where does the ball hit the ground after bounce?

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