when a ball falls vertically off a table it rebounds 75% of its height after each bounce. if it travels a total of 490 cm, how high was the table top above the floor

Answer 1

did you make a sketch

Let the height of the table be x cm
I see the ball doing this

x + 2x(.75) + 2x(.75)^2 + 2x(.75)^3 + ... = 490

x + 2x[.75 + .75^2 + .75^3 + ...] = 490

the sequence inside my square brackets is an infinite series with a=.75 and r=.75
A∞ = a/(1-r) = .75/(.25) = 3

so x + 2x(3) = 490
x = 70
so the table is 70 cm high.