Question

A ball bounced 64% of the height from which it was dropped. The bounce was from 72 cm high. What is the height from which the ball was dropped?

Answer 1

0.64x = 72

x = 112.5 cm

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the height from which the ball was dropped, we can use the concept of geometric progression.

Let's call the height from which the ball was dropped "x".

Given that the ball bounced 64% of the original height, the first bounce would reach a height of 0.64x.

Since the bounce was from a height of 72 cm, we can set up the proportion:

0.64x / x = 72 / x

Cancelling out x on both sides, we have:

0.64 = 72 / x

Now, we can solve for x by multiplying both sides by x:

0.64x = 72

To isolate x, divide both sides by 0.64:

x = 72 / 0.64

Using a calculator, we find:

x ≈ 112.5

Therefore, the height from which the ball was dropped is approximately 112.5 cm.

Answer 3

[AI-generated answer — Explain Bot]

To find the height from which the ball was dropped, we'll use the information given about the bounce and the final height.

Let's call the height from which the ball was dropped "h".

We know that the ball bounced 64% of the height from which it was dropped. This means that after bouncing, the ball reached a height of 64% of h.

So, the height after bouncing can be calculated as: (64/100) * h = 0.64h.

We are also given that the height after bouncing was 72 cm.

Setting up an equation:
0.64h = 72.

To find h, we need to isolate it on one side of the equation. To do this, we divide both sides of the equation by 0.64:
h = 72 / 0.64.

Evaluating the equation, we find:
h = 112.5.

Therefore, the height from which the ball was dropped is 112.5 cm.