A soccer player heads the ball and sends it flying vertically upwards at a speed of

24

24 m/s. If the acceleration of gravity is a= -9.8m/s2, how high above the players’ head is the ball after

2

2s?

To solve the problem of determining how high the ball is above the player's head after \( t = 2 \) seconds, we can use the following kinematic equation for vertical motion:

\[
h = v_0 t + \frac{1}{2} a t^2
\]

Where:
- \( h \) is the height above the player's head.
- \( v_0 = 24 \, \text{m/s} \) is the initial velocity of the ball.
- \( a = -9.8 \, \text{m/s}^2 \) is the acceleration due to gravity (negative because gravity opposes the upward motion).
- \( t = 2 \, \text{seconds} \) is the time.

### Step-by-Step Calculation:

1. **Substitute the known values into the equation:**
   \[
   h = 24 \times 2 + \frac{1}{2} \times (-9.8) \times (2)^2
   \]

2. **Simplify the terms:**
   \[
   h = 48 + \frac{1}{2} \times (-9.8) \times 4
   \]

3. **Calculate the gravitational term:**
   \[
   h = 48 + \frac{1}{2} \times (-39.2) = 48 - 19.6
   \]

4. **Final height:**
   \[
   h = 28.4 \, \text{meters}
   \]

Thus, after 2 seconds, the ball is **28.4 meters** above the player's head.

---

Would you like further details or have any additional questions?

Here are 5 related questions:
1. How long will the ball take to reach its highest point?
2. What is the maximum height the ball reaches above the player’s head?
3. How fast will the ball be moving after 2 seconds?
4. What is the total time the ball remains in the air before coming back to the player?
5. How high will the ball be after 3 seconds?

**Tip:** To find the maximum height of an object in free fall, set its velocity to zero and solve for time.

A soccer player heads the ball and sends it flying vertically upwards at a speed of 24 m/s. If the acceleration of gravity is -9.8 m/s², how high above the players’ head is the ball after 2 seconds?

Learn how to calculate the height of a soccer ball after 2 seconds when it is headed upwards at a velocity of 24 m/s. This kinematics problem involves applying the formula h = v₀t + (1/2)at² with a gravity of -9.8 m/s². Suitable for high school physics students in 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