While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20?

Solution 34E Step 1: In this question a ball in rolling down an inclined plane, which rolls down a distance of 1 cubit for 10 counts, we need to find the the distance travelled by the ball when the time us twice its initial time , that is after 20 counts Step 2 : Let us consider the data given Distance travelled d =11 cubit Time taken t = 10 counts 1 Acceleration down inclined plane a We need to find distance d = 2 after time t = 202counts Distance is given by d = a×t2 2 For initial 10 counts distance travelled is 2 a×(1 ) d 1 2 = 1 cubit ------------(1) For 20 counts distance travelled is 2 d = a×(2×1 ) 2 2 a×t ×(2 ) d = 1 ---------------(2) 2 2 a×(t ) From equation (1) we know 2 = d 1 , let us substitute this value in equation (2) 2 d2= d ×12 Again substitute for 1 = 1 cubit d = 1 cubit × 4 2 d2= 4 cubit