B is at ( 15,15 ) one second after colliding with A . ( c ) Find the velocity vector of B .
� 3 �
A changes its velocity to � � after the collision . It is given that A is at ( 21 , 3 ) x ��3� seconds after collision .
( d ) Find x .
( e ) Find the angle between the velocity vectors of A and B .
It is given that the horizontal edge of the table is given by the equation y � 24 .
[ 2 ]
[ 2 ]
[ 3 ]
( f ) Find the amount of time needed for B to reach the edge after A starts its motion . [ 3 ]
3 . Two planes A and B are going to land on an airport . The airport and the surrounding region can be modelled by a three-dimensional coordinate plane , where 1 unit on the coordinate axes represents 1 km . At 8:00 , A is 8 km above the position ( � 800,160 ) . It aims to land at the position ( 0 , 20 , 0 ) at 10:00 . Let t be the number of hours after 8:00 .
( a ) Find the velocity vector of A . [ 2 ]
( b ) Find the speed of A . [ 2 ]
( c ) Write down the vector equation for the displacement of A , giving the answer in the form r �a �tb , [ 2 ]
� �880� �300� � � � �
The vector equation of B is given by r � �180 � t 60 .
� 15 � � �5
� � � � �
8
( d ) Find the time when B lands on the ground . [ 2 ]
( e ) Hence , find the coordinates of B when it lands on the ground .
[ 2 ]
After A is landed on the airport at 10:00 , an electric car is going to pick up passengers from A to the terminal . The velocity vector of the car is number of hours after 10:00 .
2
� 5s
� 2s �
�
2 �, where s is the
�4s�10s �
( f ) Find the time for the car to stop again after 10:00 . [ 3 ] www . seprodstore . com
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