Bouncing ball

As the ball reaches 1/4 of total height after each bounce.

So total distance traveled is ${ S }_{ \infty }=2h+\frac { 2h }{ 4 } ............$

Now total time taken is ${ T }_{ \infty }=2\sqrt { \frac { 2h }{ g } } +2\sqrt { \frac { h }{ 2g } } +..........................$

Using the formula of sum of infinite geometric series we get

${ S }_{ \infty }=\frac { 8h }{ 3 }$

${ T }_{ \infty }=4\sqrt { \frac { 2h }{ g } }$

$\frac { { S }_{ \infty } }{ { T }_{ \infty } } =\frac { \sqrt { 2gh } }{ 3 }$

On putting values we get $4m/s$

Using sum to infinity,distance traveled by the ball equals 7.2/1-0.25=9.6. However since the ball travels twice total distance traveled needs to multiply by 2=19.2. Sum to infinity of time is 4.8 s. Therefore 19.2/4.8=4