To find the horizontal and vertical components of the velocity vector, we can follow the same method as before.

Given:

• Initial velocity $v_0 = 960 \, \text{ft/s}$
• Angle of projection $\theta = 30^\circ$

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, I will compute the values.# Given values for the cannonball problem v0_cannonball = 960 # ft/s theta_cannonball = 30 # degrees

Converting degrees to radians

theta_cannonball_rad = math.radians(theta_cannonball)

Horizontal and vertical components of the velocity

v_x_cannonball = v0_cannonball * math.cos(theta_cannonball_rad) v_y_cannonball = v0_cannonball * math.sin(theta_cannonball_rad)

Rounding the answers to two decimal places

v_x_cannonball_rounded = round(v_x_cannonball, 2) v_y_cannonball_rounded = round(v_y_cannonball, 2)

v_x_cannonball_rounded, v_y_cannonball_roundedThe horizontal and vertical components of the velocity vector of the cannonball are:

• Horizontal component: $831.38 \, \text{ft/s}$
• Vertical component: $480.00 \, \text{ft/s}$

Would you like more details or have any questions?

Here are 5 related questions:

1. What would be the time of flight for the cannonball based on the vertical component?
2. How can you calculate the maximum height the cannonball will reach?
3. What is the range of the cannonball based on these components?
4. How does changing the angle affect the flight time and range of the cannonball?
5. What if the initial velocity was increased—how would that impact both components?

Tip: The vertical component is key in determining how long a projectile stays in the air, while the horizontal component controls how far it travels.