A ball is dropped from a height of 80 metres. After hitting the ground, it bounces back to 60% of the height Class 9

A ball is dropped from a height of 80 metres. After hitting the ground, it bounces back to 60% of the height Class 9

Question 1.

A ball is dropped from a height of 80 metres. After hitting the ground, it bounces back to 60% of the height from which it fell. It continues bouncing in this way-each time rising to 60% of the previous height. Class 9

i. What height does the ball reach after the 5^th bounce?

ii. What is the total vertical distance the ball has travelled by the time it hits the ground for the 6^th time?

Solution:

Initial height = 80 m

Common ratio r = 60% = 0.6

∴ a = 80 × 0.6 = 48 m (height after 1stbounce)

i. Height after 5^th bounce

t₅ = ar^5-1

∴ t₅ = 48 × (0.6)⁴

∴ t₅ = 48 × 0.1296

∴ t₅ = 6.2208 ≈ 6.22 m

∴ The ball reach 6.22 m height after the 5^th bounce.

ii.

∴ Total vertical distance

= First fall + 2 × (sum of next 5 heights)

= 80 + 2(48 + 28.8 + 17.28 + 10.368 + 6.2208)

= 80 + 2(110.6688)

= 80 + 221.3376

= 301.3376 m = 301.34 m

∴ Total vertical distance is 301.34 m.