The Total Vertical Distance of a Ball Dropping from 10 Feet

[apiwowar]

a ball is dropped from a height of 10 feet, each bounce is 3/4 of the height of the bounce before

a)find an expression for the height h_n to which the ball rises after it hits the floor for the nth time

so h_n= 10(3/4)ⁿ

b) find an expression for the vertical distance D_i the ball has traveled when it hits the floor for the first, second, third, and fourth times.

im a little confused on this part, how would D_i relate to h_h? or do they even relate at all?

would it be 10 + 10(3/4)ⁿ since after it hits the ground the first time it will decrease by 3/4 of the previous height each time?

c) find an expression for the total vertical distance the ball has traveled when it hits the floor for the nth time

im sure once figure out b this will make perfect sense

any hints or tips on how to do this would really be appreciated.

 

[Dick]

The first time it hits the floor it's traveled 10*(3/4)^0=10 feet. The second time it's traveled 10*(3/4)^0+2*10*(3/4)^1. The '2' is because it goes up and down. The third, 10*(3/4)^0+2*10*(3/4)^1+2*10*(3/4)^2. Etc. For the first few times you can just add it up by hand. For the nth time you have to sum the geometric series.