Aball is dropped from an initial height and allowed to bounce repeatedly. on the first bounce (one up-and-down motion), the ball reaches a height of 32 inches. on each successive bounce, the ball reaches 75% of its previous height. what is the total vertical distance that the ball travels in 10 bounces? (do not include the initial height from which the ball is dropped.)

S₁₀ = 241.5837 m

Explanation:

If

h₁ = 2*32 in = 64 in

h₂ = 0.75*h₁ = (0.75)*64 in = 48 in

h₃ = 0.75*h₂ = 0.75*(0.75*h₁) = (0.75)²*h₁ = (0.75)²*64 in = 36 in

h₄ = 0.75*h₃ = 0.75*(0.75*h₁) = (0.75)³*h₁ = (0.75)³*64 in = 27 in

...

h₁₀ = 0.75*h₉ = (0.75)⁹*h₁ = (0.75)⁹*64 in = 4.8054 in

It is a geometric sequence (geometric progression) where the common ratio is

r = 0.75

Finding the sum of terms in a geometric progression is easily obtained by applying the formulas:

10th partial sum of a geometric sequence

S₁₀ = h₁*(1 - r¹⁰) / (1 - r)

⇒   S₁₀ = 64*(1 - 0.75¹⁰) / (1 - 0.75)

⇒   S₁₀ = 241.5837 m

sonar - device which is used to find the submit submarines, sankalp ship. sonar waves consists of a transmitter and detector which are installed in the observation centre on board of a ship. the ultrasonic waves are sent into the sea at high frequency about 1000 khz in all direction.

one person pulls 90n one way and the other has 100n pulling the other way.

so the net force = 90 - 100 = -10n,

or the ans can be 10n if the picture shows -90n and 100n instead.