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

Answer:

28.75 m.

Step-by-step 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 $a_2=2\times (\dfrac{50}{100}\times 10)=2(5)=10\ m$

Similarly,

For third bounce the vertical distance $a_3=2\times (\dfrac{50}{100}\times 5)=2(2.5)=5\ m$

For fourth bounce the vertical distance $a_4=2\times (\dfrac{50}{100}\times 2.5)=2(1.25)=2.5\ m$

For fifth bounce the vertical distance $a_5=2\times (\dfrac{50}{100}\times 1.25)=2(0.625)=1.25\ m$

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.