A ball is dropped from a height of 24 meters Each time it st

A ball is dropped from a height of 24 meters. Each time it strikes the ground it bounces back vo a height of three-fourths the distance from which it fell. Determine the total dblanct Inverted by the before it comes to rest. Show all work. 2, 6, (5x + 3),... is a given sequence showing the first three terms. Find a value of x so that ihe sequence will be

Solution

10)total distance travelled by the ball =24 +(3/4)(24+24) + (3/4)²(24+24) +..........

total distance travelled by the ball =24 +(3/4)48 + (3/4)²48 +..........

total distance travelled by the ball =24 +48[(3/4) + (3/4)² +..........]

sum of infinate geometric series is a/(1-r) when r<1.

a=3/4 , r =3/4

total distance travelled by the ball =24 +48[(3/4)/(1-(3/4))]

total distance travelled by the ball =24 +48[(3/4)/(1/4)]

total distance travelled by the ball =24 +(48*3)

total distance travelled by the ball =168m