A hockey player's arm and stick form a 1.6 m rigid segment. If the angular speed of the player's arm/stick is 1.2 rad/s, determine the resultant velocity of a motionless puck that is hit struck on if:
a) the hockey player is stationary during the swing
b) the hockey player is moving forwards at 3 m/s
To determine the resultant velocity of the puck, we need to consider the angular speed of the player's arm/stick and the linear velocity of the player.
a) If the hockey player is stationary during the swing, the angular speed of the arm/stick is solely responsible for the motion of the puck. We can calculate the velocity of the puck using the formula:
Velocity of the Puck = Angular Speed of the Arm/Stick * Radius
In this case, the radius would be the length of the rigid segment formed by the arm and stick, which is given as 1.6 m. The angular speed is given as 1.2 rad/s.
Velocity of the Puck = 1.2 rad/s * 1.6 m
Velocity of the Puck = 1.92 m/s
Therefore, if the hockey player is stationary during the swing, the resultant velocity of the motionless puck would be 1.92 m/s.
b) If the hockey player is moving forwards at 3 m/s during the swing, we need to consider both the angular speed of the arm/stick and the linear velocity of the player. In this case, we can calculate the resultant velocity using vector addition.
Resultant Velocity = Velocity of the Puck + Velocity of the Player
The velocity of the player is given as 3 m/s, and the velocity of the puck can be calculated as in part a) using the formula:
Velocity of the Puck = Angular Speed of the Arm/Stick * Radius
Velocity of the Puck = 1.2 rad/s * 1.6 m
Velocity of the Puck = 1.92 m/s
Therefore, the resultant velocity of the puck when the hockey player is moving forwards at 3 m/s during the swing would be:
Resultant Velocity = 1.92 m/s + 3 m/s
Resultant Velocity = 4.92 m/s
Thus, the resultant velocity of the motionless puck when the hockey player is moving forwards at 3 m/s during the swing would be 4.92 m/s.