Question

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 1

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