A child drops a ball from a window 5.0 m above the ground…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A child drops a ball from a window above the ground. It bounces once, and she catches it on the way up, above the ground.
- What is the path length of the ball, from the drop to the catch?
- What is its displacement?
Need a reminder? The key ideaShow
Path length adds up every metre travelled, whatever the direction; it is never negative. Displacement is the change of position, with a sign:
Take the ground as the origin and up as positive.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Dropped from , caught at , with up positive.
Plan. Add the two legs for the path length; subtract the positions for the displacement.
Step 1. Path length. Down , then up : .
Step 2. Displacement. : below the window.
Answer: (a) . (b) , that is downwards.
Check. The size of the displacement, , is less than the path length, as it must be when the ball turns back.
Watch out. The bounce does not cancel anything in the path length: going down and coming up both add.
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