Question

A ball is dropped from a height of 80ft the ball is such that it rebounds (3/4)th of the height it has fallen . How high does the ball on 6th bounce? How high ball rebound on nth bounce?

Answer 1

Answer:

rebound on nth bounce = 60 * (3/4)ⁿ⁻¹  = 80 (3/4)ⁿ  ft

Rebound on 6th bounce = 60 * (3/4)⁵ = 14.24 ft

Step-by-step explanation:

A ball is dropped from a height of 80ft the ball is such that it rebounds (3/4)th of the height it has fallen . How high does the ball on 6th bounce? How high ball rebound on nth bounce?

Ball Dropped from 80 ft

it rebounds (3/4)th of the height it has fallen

on 1st rebound = 80(3/4) = 60 ft

on 2nd rebound = 60(3/4) = 45 ft

on 3rd rebound = 45(3/4) ft

its an GP

Where a = 60 ft

r = 3/4

rebound on nth bounce = 60 * (3/4)ⁿ⁻¹  = 80 (3/4)ⁿ  ft

Rebound on 6th bounce = 60 * (3/4)⁵ = 14.24 ft

Answer 2

The height in successive bounce form a G.P with r = 3/4

Since the ball is dropped from a height of 80 ft, therefore height at the first bounce is given by

$a = 80 \times \frac{3}{4}$

Height in the 6th bounce

$= {ar}^{6 - 1}$

$= 80 \times \frac{3}{4} \times ({ \frac{3}{4} })^{5}$

$= 80( { \frac{3}{4} })^{6} ft$

Height in the n th bounce

$= {ar}^{n - 1}$

$= 80 \times { \frac{3}{4} }^{n} ft$

Hope it helps!!✔✔