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The height of a ball is h(t) = 20t - 4.9t² metres…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The height of a ball is metres. Make 821 equally spaced times from 0 to 4.1 s. Find the slope of with np.gradient, find where it changes sign, and give the time and the height of the top. Check the time with the formula .
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.
Plan. The top of the path is where the slope is zero, so the sign of the slope changes there.
Check. The formula gives s and m. The grid has a point every 0.005 s, so the nearest are 2.040 s and 2.045 s. The program finds the sign change at 2.04 s and a height of 20.41 m.
Answer: the top is at about 2.04 s, at a height of 20.41 m.
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