Imagine a ball rolls off a set of stairs with horizontal velocity, u; the stairs have a height, h and length of l. Find a formula for which step the ball will hit, n.
We set up equations in horizontal and vertical directions assuming constant acceleration due to gravity, g. It is always useful to draw a diagram to see what's going on. Using the SUVAT formula of s = ut + 1/2at^2 in both directions, we obtain equations of; vertical: s_y = nh = 1/2gt^2, horizontal: s_x = nl = u_0*t. We now eliminate t from these equations (by substitution) and make n the subject of the formula. Solving gives: n = (2hu^2)/(gl^2).
I wanted to go through some examples using this which involves some physics thinking of the problem, i.e. what happens in cases of u = 1.5 m/s with h = l = 0.2 m, and the case of u = 3 m/s with h = l = 0.2 m.
JB
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