Question

A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50% of its previous height. The total vertical distance down the ball has traveled when it hits the the 5th time is how many meters

Answer 1

28.75 m.

Explanation:

It is given that a ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50% of its previous height. So,

For first bounce the vertical distance
`a_1= 10\ m`

For next bounce ball has to travel up and down by 50% of previous distance, i.e., 10 m.

For second bounce the vertical distance
`a_2=2* ((50)/(100)* 10)=2(5)=10\ m`

Similarly,

For third bounce the vertical distance
`a_3=2* ((50)/(100)* 5)=2(2.5)=5\ m`

For fourth bounce the vertical distance
`a_4=2* ((50)/(100)* 2.5)=2(1.25)=2.5\ m`

For fifth bounce the vertical distance
`a_5=2* ((50)/(100)* 1.25)=2(0.625)=1.25\ m`

The total vertical distance down the ball has traveled when it hits the the 5th time is

`\text{Total distance}=a_1+a_2+a_3+a_4+a_5`

`\text{Total distance}=10+10+5+2.5+1.25`

`\text{Total distance}=28.75\ m`

Therefore, the total vertical distance down the ball has traveled when it hits the the 5th time is 28.75 m.