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 [tex]a_1= 10\ m[/tex]
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 [tex]a_2=2\times (\dfrac{50}{100}\times 10)=2(5)=10\ m[/tex]
Similarly,
For third bounce the vertical distance [tex]a_3=2\times (\dfrac{50}{100}\times 5)=2(2.5)=5\ m[/tex]
For fourth bounce the vertical distance [tex]a_4=2\times (\dfrac{50}{100}\times 2.5)=2(1.25)=2.5\ m[/tex]
For fifth bounce the vertical distance [tex]a_5=2\times (\dfrac{50}{100}\times 1.25)=2(0.625)=1.25\ m[/tex]
The total vertical distance down the ball has traveled when it hits the the 5th time is
[tex]\text{Total distance}=a_1+a_2+a_3+a_4+a_5[/tex]
[tex]\text{Total distance}=10+10+5+2.5+1.25[/tex]
[tex]\text{Total distance}=28.75\ m[/tex]
Therefore, the total vertical distance down the ball has traveled when it hits the the 5th time is 28.75 m.
