Relative Motion of a hockey player

[wallace13]

Mario, a hockey player, is skating due south at a speed of 7.1 m/s relative to the ice. A teammate passes the puck to him. The puck has a speed of 12.9 m/s and is moving in a direction of 20° west of south, relative to the ice. What are the magnitude and direction (relative to due south) of the puck's velocity, as observed by Mario?



Vpi + V mi = V pm



I basically have no idea how to even set up this problem, because i don't understand how the puck could be passed to him at 20 degrees west of south when he is going south. But I did 12.9 cos 20 = 59.64 degrees and 12.9 - 7.1 = 5.8 m/s for the velocity and its obviously wrong.

 

[Kurdt]

If you work out the components of velocity of the puck and subtract mario's velocity from the south component, you will then have two components of velocity of the puck from Mario's perspective and you should be able to work out the angle relative to south.

 

[baba89]

I can help clarify the situation and provide a solution. The key to understanding this problem is recognizing that the velocities are relative to different frames of reference. Mario's velocity of 7.1 m/s is relative to the ice, while the puck's velocity of 12.9 m/s is also relative to the ice. However, the puck's direction is given relative to Mario's direction of travel, which is due south. This means that the puck's direction is actually at an angle of 20° west of south from Mario's perspective.

To solve this problem, we can use vector addition to find the puck's velocity as observed by Mario. We can break down the puck's velocity into its x and y components, using the angle and trigonometry. The x component would be 12.9 cos 20° = 12.2 m/s and the y component would be 12.9 sin 20° = 4.5 m/s.

Now, we can add these components to Mario's velocity of 7.1 m/s to find the puck's velocity as observed by Mario. Using the Pythagorean theorem, we can find the magnitude of the puck's velocity to be 13.1 m/s. To find the direction, we can use inverse tangent to find the angle between the puck's velocity and due south. This angle is approximately 26.5° west of south.

Therefore, the magnitude of the puck's velocity is 13.1 m/s and the direction is 26.5° west of south as observed by Mario. This means that the puck is moving at a slightly faster speed and in a slightly more westward direction than Mario's own velocity. Keep in mind that this is all relative to Mario's perspective and his direction of travel.