Question

The ball was dropped from a height of 10 feet and begins bouncing. The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance travelled by the ball.
60 ft
70 ft
80 ft
90 ft​

Answer 1

Step-by-step explanation:

The ball was dropped from a height of 10 feet and begins bouncing. The height of each bounce is three-fourths the height of the previous bounce therefore the vertical distance travelled by the ball is 60 ft

Answer 2

Given:

A ball is dropped from a height of 10 feet and it keeps on bouncing. It bounces to a height of 3/4 the height of the previous bounds.

To find:

The vertical distance traveled by the ball.

Solution:

1. It is given that the ball is dropped from a height of 10 Feet. Distance covered vertically, in this case, is 10 feet.

2. The ball bounces to a height of (3/4) * 10 for the next bounce. Distance covered vertically, in this case, is  2 * (3/4) * 10. ( covers the same distance while going up and coming down).

3. In the next case, The ball bounces to a height of $\frac{3}{4} *\frac{3}{4} *10$, and it covers a vertical distance of $2*\frac{3}{4} *\frac{3}{4}$. ( Covers the same distance while going up and coming down).

4. In the next case it bounces to a height of $10*(\frac{3}{4}) ^{3}$. It covers a distance of twice its height).

• From the above steps, we can conclude that it forms an Infinite geometric progression.
• The total distance covered by the ball vertically is given as :

10 + 2* (sum of the infinite Geometric progression) [ it is multiplied by 2 because it is covering the distance twice i.e while going up and while coming down].

=> Total vertical distance travelled = 10 + 2*Sum of infinite GP.

5. Sum of an infinite Geometric progression with first term a and common ratio r is given as  : $\frac{a}{1-r}$

6. On substituting the data in the given formula i.e, a = 30/4 and r = 3/4 we get,

=> S (infinite terms) = 30.

7. Therefore the total distance covered by the ball is 10 + 2* 30 = 70ft.

Therefore, The total vertical distance traveled by the ball is 70ft (Option C).