Final answer:
The horizontal component of the initial velocity of the cannonball is approximately 93.97 m/s, and the vertical component is approximately 34.20 m/s, calculated using trigonometric functions based on the given launch speed and angle.
Step-by-step explanation:
The student is asking about the horizontal and vertical components of the initial velocity of a cannonball fired from a cannon. When a projectile is launched at an angle, its initial velocity can be broken down into horizontal (x) and vertical (y) components using trigonometric functions. For an initial speed of 100 m/s at an angle of 20° above the horizontal:
- The horizontal component (vx) is found using the cosine function: vx = v × cos(θ) = 100 m/s × cos(20°).
- The vertical component (vy) is found using the sine function: vy = v × sin(θ) = 100 m/s × sin(20°).
Using a calculator, this gives:
- vx = 100 m/s × 0.9397 ≈ 93.97 m/s (to two decimal places)
- vy = 100 m/s × 0.3420 ≈ 34.20 m/s (to two decimal places)
Therefore, the horizontal component of the initial velocity is approximately 93.97 m/s, and the vertical component is approximately 34.20 m/s.