https://file.aiquickdraw.com/mathbot/file/1729777784871mc686cz9.jpg

Let's break down and solve each of the problems based on the image you provided. I'll guide you through the solution and then fill out the tables for each.

### Problem 1:
A volleyball is hit straight up into the air with an initial velocity of \( v_0 = 6.0 \, \text{m/s} \), starting from a height of \( y_0 = 2.0 \, \text{m} \) above the ground. We need to determine how long the ball will be in the air before it strikes the floor. We'll assume that the acceleration \( a \) is due to gravity, \( a = -9.8 \, \text{m/s}^2 \).

#### Steps to solve:
1. **Find the time when the ball reaches the highest point** (when \( v = 0 \)):
   \[
   v = v_0 + at
   \]
   At the highest point, \( v = 0 \):
   \[
   0 = 6.0 + (-9.8)t \quad \Rightarrow \quad t = \frac{6.0}{9.8} \approx 0.61 \, \text{seconds}.
   \]
   This is the time to reach the maximum height.

2. **Find the maximum height**:
   \[
   y_{\text{max}} = y_0 + v_0 t + \frac{1}{2} a t^2
   \]
   Substituting the values:
   \[
   y_{\text{max}} = 2.0 + 6.0(0.61) + \frac{1}{2}(-9.8)(0.61)^2 \approx 2.0 + 3.66 - 1.83 \approx 3.83 \, \text{m}.
   \]

3. **Find the time to fall back down from the maximum height to the ground**:
   Use the equation \( y = y_0 + v_0 t + \frac{1}{2} a t^2 \), where \( y = 0 \) (since it's hitting the ground).
   \[
   0 = 3.83 + 0 t + \frac{1}{2}(-9.8)t^2
   \]
   Solving for \( t \):
   \[
   t^2 = \frac{2(3.83)}{9.8} \quad \Rightarrow \quad t \approx 0.88 \, \text{seconds}.
   \]
   So, the total time to fall back down is 0.88 seconds.

4. **Total time in the air**:
   The total time is the sum

A volleyball is hit straight up into the air with an initial velocity of 6.0 m/s. If the volleyball starts from 2.0 m above the floor, how long will it be in the air before it strikes the floor? What is the highest point above the ground that the ball will reach? If a different volleyball was hit from a height of 0.80 m above the floor with an initial velocity of 7.5 m/s, how high will it go?

Learn how to solve projectile motion problems for a volleyball hit straight up with different initial velocities. This problem involves calculating the total time in the air and maximum height using kinematics equations. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation