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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12
A player P kicks the football with velocity 20 m/s at angle of 15°. Another player Q on the goal line 12 m away in the direction of kick, runs at the same instant to meet the ball. With what speed he should run so that he could catch the ball just before it hits the ground? (Take g = 10 m/s2).

We know that,

Horizontal range, straight R equals fraction numerator straight u squared sin 2 straight theta over denominator straight g end fraction

We have,

Initial space velocity comma space straight u equals 20 straight m divided by straight s

Angle space of space projecvtion comma space straight theta equals 15 degree

a c c e l e r a t i o n space d u e space t o space g r a v i t y comma space straight g equals 10 space straight m divided by straight s squared

∴  

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i.e. the ball hits the ground at a distance of 20m from the position of player P.

Since the player Q is 12m away, therefore, he has to travel a distance 8m to catch the ball in time equal to the time of flight.

Now the time of flight is,

        space space space space straight T equals fraction numerator 2 straight u space s i n theta over denominator straight g end fraction
space space space space space space equals fraction numerator 2 cross times 20 cross times s i n 15 degree over denominator 10 end fraction
space space space space space space space equals 4 s i n 15 degree

rightwards double arrow       straight T equals 1.035 space straight s 

The velocity of player Q is,

     straight v equals fraction numerator 8 over denominator 1.035 end fraction equals 7.727 space straight m divided by straight s

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