A (field) hockey player is running north at a speed of 8 m/s . A ball

1.	A (field) hockey player is running north at a speed of 8 m/s . A ball is coming directly towards her from the north at a speed of 18 m/s. She swings her stick forward, directly north, at a speed of 6 m/s measured in her own frame of reference. What is the speed of the ball with respect to the hockey stick? Relative to the hockey stick, the ball is travelling at ____ m/s.
Answer» Answer: The ball is travelling at -24 m/s Explanation: At first, we should choose a common frame of reference. Here, we use the FIELD as the common frame of reference. This is because it is stationary with RESPECT to everything else. Player velocity ( $V_p$ ) = +8 relative to the field. STICK velocity ( $V_s$ ) = +6 + $V_p$ = +6 + +8 = +14 relative to the field. It is unclear whether the ball’s velocity is relative to the field or the player. Case 1: Ball velocity ( $V_b$ ) = -18 relative to the field. Ball velocity relative to the stick is $V_b - V_s$ $V_b - V_s$ = (-18) - (+14) = -32 m/s Case 2: Ball velocity ( $V_b$ ) = -18 relative to the player. Ball velocity ( $V_b$ ) relative to the field is the SUM: $V_b$ = (-18) + $V_p$ = -18 + 8 = -10 As in case 1, ball velocity relative to the stick, $V_b - V_s$ = (-10) - (+14) = -24 m/s ∴ Relative to the hockey stick, the ball is travelling at -24 m/s

A (field) hockey player is running north at a speed of 8 m/s . A ball is coming directly towards her from the north at a speed of 18 m/s. She swings her stick forward, directly north, at a speed of 6 m/s measured in her own frame of reference. What is the speed of the ball with respect to the hockey stick? Relative to the hockey stick, the ball is travelling at ____ m/s.

Answer»

Answer:

Explanation:

Player velocity ( $V_p$ ) = +8 relative to the field.

STICK velocity ( $V_s$ ) = +6 + $V_p$ = +6 + +8 = +14 relative to the field.

It is unclear whether the ball’s velocity is relative to the field or the player.

Case 1:

Ball velocity ( $V_b$ ) = -18 relative to the field.

Ball velocity relative to the stick is $V_b - V_s$

$V_b - V_s$ = (-18) - (+14) = -32 m/s

Case 2:

Ball velocity ( $V_b$ ) = -18 relative to the player.

Ball velocity ( $V_b$ ) relative to the field is the SUM:

$V_b$ = (-18) + $V_p$ = -18 + 8 = -10

$V_b - V_s$ = (-10) - (+14) = -24 m/s