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A rugby player runs with the ball directly toward his opponent's goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball's velocity relative to the field does not have a positive x component. Suppose the player runs at speed 5.9 m/s relative to the field while he passes the ball with velocity vector v BP relative to himself. If vector v BP has magnitude 7 m/s, what is the smallest angle it can have for the pass to be legal?1° (relative to +x axis)



Answer :

If he passes the ball with a velocity vector v BP relative to himself, and v BP has a value of 7 m/s, then the least angle it can have is 32.5 °.

A player runs at a speed relative to field is  v1  = 5.9 m/s

A player runs at a speed relative to himself  is  v2  = 7 m/s

                v  = v_1 +v_2

                     = 5.9 m/s + 7.0 m/s

                       = 12.9 m/s

smallest angle by  which the player hits the ball is θ  = cos^-1 ( 5.9 / 7.0)

                                                                                           = 32.5 degrees

Velocity is the rate at which an object is changing position when it is observed from a certain point of view and as measured by a particular unit of time. It is defined as the direction at which an object is traveling. Speed is the rate of movement along a path in contrast to velocity, which specifies the direction and speed of an object's motion.

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