Physics Problem Help

The time shown on a clock changes from 4:00 to 4:30 . The minute hand, of length 25cm , moves smoothly halfway around the face. The movement of the tip of the minute hand can be thought of as lots of small displacement vectors taking the tip from the old to the new position.
For the tip of the minute hand, what is the average downward displacement of the tip, over the half hour, from its position at 4:00 ?
This probably looks like it involves integration, but I have no idea how to go about it/set it up. Please could someone walk me through the steps to the answer. Thanks.

The time shown on a clock changes from 4:00 to 4:30 . The minute hand, of length 25cm , moves smoothly halfway around the face. The movement of the tip of the minute hand can be thought of as lots of small displacement vectors taking the tip from the old to the new position.
For the tip of the minute hand, what is the average downward displacement of the tip, over the half hour, from its position at 4:00 ?
This probably looks like it involves integration, but I have no idea how to go about it/set it up. Please could someone walk me through the steps to the answer. Thanks.

The time shown on a clock changes from 4:00 to 4:30 . The minute hand, of length 25cm , moves smoothly halfway around the face. The movement of the tip of the minute hand can be thought of as lots of small displacement vectors taking the tip from the old to the new position.
For the tip of the minute hand, what is the average downward displacement of the tip, over the half hour, from its position at 4:00 ?
This probably looks like it involves integration, but I have no idea how to go about it/set it up. Please could someone walk me through the steps to the answer. Thanks.

You would probably use circular motion for this right? You can calculate angular frequency by 2pi/T, where T=60x60, then calculate v=r x omega. You would then integrate v w.r.t t from t=0 to t=30x60. I don’t think this the right way of solving it.

If you were to think about vectors in terms of polar coordinates, you would end up with v pointing in the phi hat direction (take r hat to point outwards from the centre of the clock, along the minute hand; phi hat points in the clockwise direction, and k hat points into the clock face). This doesn’t sound promising because you would then have to integrate phi hat (because it too changes with time, along with r hat)
*r hat, phi hat and k hat are unit vectors along those directions

I just realised something- you can convert phi hat back to Cartesian coordinates once you’re done with all the cross products involved with calculating v. So now, you can easily integrate the velocity vector to get displacement. The whole thing with AVERAGE displacement can be dealt with by dividing the integral by the time period I believe (30 mins in this case)

I really think youre overcomplicating it. Just draw a clock at 4 and 4.30 and measure the vertical displacement of the minute hand and divide by 30.

I just realised something- you can convert phi hat back to Cartesian coordinates once you’re done with all the cross products involved with calculating v. So now, you can easily integrate the velocity vector to get displacement. The whole thing with AVERAGE displacement can be dealt with by dividing the integral by the time period I believe (30 mins in this case)

I tried that, but 50/30 was wrong. No idea what the correct answer is still. Any help?

Have you got a link to the question?

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Okay so apparently average displacement = median displacement.
So the displacement (vertical) of the minute hand goes from 0 --> 50cm, so the "average" is 25cm.