A quarterback throws a football with angle of elevation 40 and speed 60 ft/s/ find the horizontal and vertical components of the velocity vector

To find the horizontal and vertical components of the velocity vector for the football, we can use trigonometric functions, specifically sine and cosine, along with the given angle of elevation and the speed.

The angle of elevation is \( \theta = 40^\circ \) and the speed (magnitude of the velocity) is \( v = 60 \, \text{ft/s} \).

### Formulas:
- Horizontal component: \( v_x = v \cdot \cos(\theta) \)
- Vertical component: \( v_y = v \cdot \sin(\theta) \)

Now, let's calculate the components:

1. **Horizontal component**:
\[
v_x = 60 \cdot \cos(40^\circ)
\]

2. **Vertical component**:
\[
v_y = 60 \cdot \sin(40^\circ)
\]

I'll compute these values.The components of the velocity vector are:

- **Horizontal component**: \( v_x \approx 45.96 \, \text{ft/s} \)
- **Vertical component**: \( v_y \approx 38.57 \, \text{ft/s} \)

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How do the horizontal and vertical components change with a different angle?
2. How does the velocity change if the initial speed is increased?
3. What is the total time the football stays in the air?
4. How far does the football travel horizontally (range)?
5. How high does the football go (maximum height)?

**Tip**: The horizontal component of velocity remains constant in projectile motion if air resistance is neglected.

A quarterback throws a football with angle of elevation 40 and speed 60 ft/s. Find the horizontal and vertical components of the velocity vector.

Learn how to find the horizontal and vertical components of velocity for a football thrown at an angle of elevation of 40 degrees and a speed of 60 ft/s. This problem covers key concepts in trigonometry and projectile motion. Suitable for students in Grades 9-12.

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