Question

5th question solution

Answer 1

The total distance travelled by the ball is
$h + 2 \times (h r) + 2 \times (h {r}^{2} ) + ..... \\ = h \times (1 + 2r(1 + r + {r}^{2} + ......)) \\ = h \times (1 + \frac{2r}{1 - r} ) \\ = h \times ( \frac{1 + r}{1 - r} ) \\ = 3 \times ( \frac{1 + \frac{2}{3} }{1 - \frac{2}{3} } ) = 3 \times \frac{5}{1} = 15 \: m$
Note: Multiplying by 2 in the first line is because whatever height the ball bounces, it will come back to the ground by travelling same distance