When a ball bounces it it rises to 3 upon 4 the of the height from which it fell it the ball is dropped from the height of 32 m how height will it rises at the third bounce?

To find the height to which the ball rises on the third bounce, we can use the following approach:

1. **Initial Height**: The ball is dropped from a height of \( 32 \) meters.

2. **Height after the First Bounce**: The ball rises to \( \frac{3}{4} \) of the height it fell from. So, after the first bounce:
   \[
   h_1 = \frac{3}{4} \times 32 = 24 \text{ meters}
   \]

3. **Height after the Second Bounce**: The ball again rises to \( \frac{3}{4} \) of the height after the first bounce. So, after the second bounce:
   \[
   h_2 = \frac{3}{4} \times 24 = 18 \text{ meters}
   \]

4. **Height after the Third Bounce**: Similarly, after the third bounce:
   \[
   h_3 = \frac{3}{4} \times 18 = 13.5 \text{ meters}
   \]

So, the ball will rise to a height of **13.5 meters** on the third bounce.

Would you like more details or have any specific questions about this problem? Here are some related questions to explore further:

1. What would be the height after the fourth bounce?
2. How do you find the total distance the ball travels until it stops bouncing?
3. If the fraction of the bounce height changes, how does it affect the bounce heights?
4. Can you model this scenario using a geometric series?
5. What assumptions are we making about energy loss in each bounce?

**Tip**: When dealing with problems involving repeated actions (like bouncing), geometric sequences are often helpful in modeling the situation.

Learn how to calculate the height to which a ball rises after multiple bounces, starting from an initial height of 32 meters. This problem involves using geometric sequences to find the heights after each bounce, demonstrating applications of geometric concepts in real-world scenarios. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation