To find the horizontal and vertical components of the velocity vector, we will use trigonometric functions.

Given:

• Initial velocity $v_0 = 2049 \, \text{ft/s}$
• Angle of projection $\theta = 20^\circ$

1. Horizontal component of the velocity:

$v_x = v_0 \cdot \cos(\theta)$

2. Vertical component of the velocity:

$v_y = v_0 \cdot \sin(\theta)$

Now, let's compute these values.import math

Given values

v0 = 2049 # ft/s theta = 20 # degrees

Converting degrees to radians for trigonometric functions

theta_rad = math.radians(theta)

Horizontal and vertical components of the velocity

v_x = v0 * math.cos(theta_rad) v_y = v0 * math.sin(theta_rad)

Rounding the answers to two decimal places

v_x_rounded = round(v_x, 2) v_y_rounded = round(v_y, 2)

v_x_rounded, v_y_roundedThe horizontal and vertical components of the velocity vector are:

• Horizontal component: $1925.43 \, \text{ft/s}$
• Vertical component: $700.80 \, \text{ft/s}$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you calculate the range of the bullet using these components?
2. What is the time of flight of the bullet given the vertical component?
3. How does the angle of projection affect the horizontal and vertical components?
4. What is the significance of the horizontal component in projectile motion?
5. How would the components change if the angle was 45 degrees?

Tip: The angle of projection determines the distribution of velocity between the horizontal and vertical components—higher angles give more vertical velocity.