Re: Grade 12 Physics Problems
The each time it bounces loses 75% of its speed is a data, depend on the floor material and the ball material.
We decompose the speed in 2 speeds, one forward (->) and one up (/|).
Each of these speeds is sqrt (2) * 20 (do the math).
Now the ball accelerates downwards (|/) at 10m/s*s.
So it takes sqrt (2) * 20/10 = sqrt (2) * 2 seconds to stop going up and start going down.
In that time it moved sqrt (2) * 2 * sqrt (2) * 20 = 80m. (sqrt (2) * 2 = time, sqrt (2) * 20 = speed).
Since it has constant acceleration it describes a parabola. We know the vertex is between both roots, so that means it hits the ground again at 160m.
Now the next time, the speed will be 10m/s and the starting angle will be the same.
This means it moves 160m * 1/4, or 40m. We can keep on like this forever since it will never stop, but we do realize that it moves always slower.
So it moves
160m * (1+1/4+1/4/4+1/4/4/4.................) = 160 * (1+1/4+1/16+1/64........)
Now some math.
1 + 1/x + 1/x2 + 1/x3 + 1/x4.... 1/xn + 1/x n+1) = 1 + 1/x-1. (this applies for all x > 1)
So 160m * (1+1/4+1/4/4+1/4/4/4......................) = 160 * (1+1/4+1/16+1/64..........) = 160 * (1+1/3) = 160m * 4/3 = 640m/3.
The ball moves 640m/3. Though it actually never stops.