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# Physics/net displacement

Question
Hello. I have a question that is confusing me. I need to find how large the net displacement is.

A ball on a porch rolls 60 cm to the porch's edge, drops 40 cm, continues rolling on the grass, and eventually stops 80 cm from the porch's edge.

What is the magnitude of the ball's net displacement, in centimeters?

Hello Steven,

The net displacement depends on distance between the starting point and the ending point, not the path it took between those points. Draw a side view of the ball rolling along the porch, dropping, and rolling along the grass. Now draw a straight line from the start to the end. The question is asking for the length of that diagonal line.

Consider this addition to the drawing:
Draw a vertical line downward from the start point. Draw a horizontal line from the end point under the porch until it intersects with the vertical line you previously added. Now, do you see a right triangle? Ignore the 60 cm path along the surface of the porch and ignore the drop off the edge of the porch. The ball's displacement is the same whether it followed the path you described, or if there were a hole in the deck of the porch so that the ball dropped straight down from the start point, hit the ground and rolled horizontally out from under the porch and stopped at the end point.

So your right triangle has a 40 cm vertical side and a 140 cm horizontal side. Calculate the length of the hypotenuse.

I hope this helps,
Steve

Physics

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University