A football is kicked at 20.5 meters per second at a 31.0 degree angle to the horizon. It lands on flat ground 2.16 seconds later. How far away did the ball land? Delta x equals blank meters; fill in the blank.

To solve for how far away the football lands, we need to calculate the horizontal distance (\(\Delta x\)). We can use the following kinematic equation for horizontal motion:

\[
\Delta x = v_{0x} \cdot t
\]

Where:
- \(\Delta x\) is the horizontal distance.
- \(v_{0x}\) is the initial horizontal velocity.
- \(t\) is the time the football is in the air.

### Step 1: Calculate the horizontal velocity \(v_{0x}\)
The initial velocity (\(v_0\)) is given as 20.5 m/s, and the angle (\(\theta\)) is 31.0°. The horizontal component of the velocity can be calculated as:

\[
v_{0x} = v_0 \cdot \cos(\theta)
\]

Substitute the values:

\[
v_{0x} = 20.5 \cdot \cos(31.0^\circ)
\]

### Step 2: Calculate the horizontal distance \(\Delta x\)
Now, use the horizontal velocity and the time of flight (2.16 s) to calculate the distance.

\[
\Delta x = v_{0x} \cdot 2.16
\]

I'll calculate this for you.The football lands approximately 37.96 meters away.

Would you like more details or have any further questions?

Here are 5 related questions you might find interesting:
1. How high did the football go at its peak?
2. What was the football's vertical velocity at the time of landing?
3. How long did it take for the football to reach its highest point?
4. What would happen if the angle was changed to 45°?
5. How would the range change if the initial speed was increased to 25 m/s?

**Tip:** The optimal angle for maximum range in projectile motion (without air resistance) is 45°.

Learn how to calculate the distance a football travels when kicked at 20.5 m/s at a 31-degree angle, landing 2.16 seconds later. This problem involves kinematic equations, trigonometry, and projectile motion, suitable for Grades 9-12 physics or math students.

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