4 . A ball A is moving on a smooth table which can be modelled by a x - y plane . Its initial position is ( 0 , 0 ) . A collides with another moving ball B after two seconds . It is given that the initial position of B is ( 12 , 5 ) .
( a ) Find the initial distance between the two balls .
�4� The velocity vector of A is given by � �
�5� .
[ 2 ]
( b ) Write down the vector equation for the displacement of A , giving the answer in the form r �a �tb , where t is the time in seconds after the start of motion .
[ 2 ]
B stops moving after colliding with A .
( c ) Find the velocity vector of B .
��1�
A changes its velocity to � � after the collision . It is given that A is at � 3 �
( 5.5,17.5 ) x seconds after collision .
[ 2 ]
( d ) Find x . [ 2 ]
( e ) Find the acute angle between the two velocity vectors of A .
[ 3 ] It is given that the horizontal edge of the table is given by the equation y � 31.
( f ) Find the amount of time needed for A to reach the edge after it starts its motion .
[ 3 ]
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