Ignoring air resistance and assuming gravity to equal 9.81. If a ball of mass 1kg is dropped from a height of 100m, calculate it's final velocity before it hits the ground.
G = 9.81u = 0s = 100v2 = u2 + 2asv2 = 2 * 100 * 9.81v = root( 2 * 100 * 9.81) = 44.29ms-1
This question can be made into a 3 part question suitable for advanced A level students
B) Determine or show graphically the sum of the series T(n) = (1/2)n with N being from 1 to infinity(Ans, 1)
C) When the ball in part A hits the ground, it bounces and loses half its vertical kinetic energy. Calculate the total vertical distance travelled by the ball.
ANSFirst the ball travels 100m down, then 50m back up and 50m down, then 25m up and 25 down etc.By separating the distance between each bounce, the series goes;100, 100, 50, 25, 12.5...Ignoring the first two hundreds, the sequence is the same as 100T(n)100 + 100 + 100(T(n))Therefore the answer is 300m
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