Understanding the Problem
* Velocity is a vector quantity, meaning it has both magnitude (speed) and direction.
* The horizontal and vertical components of the initial velocity represent the ball's motion in those directions.
* We can use the Pythagorean theorem to find the magnitude (speed) of the initial velocity.
Calculations
1. Visualize: Imagine a right triangle where:
* The horizontal component (18.2 m/s) is the base.
* The vertical component (21.3 m/s) is the height.
* The hypotenuse represents the magnitude of the initial velocity.
2. Pythagorean Theorem: a² + b² = c²
* a = 18.2 m/s
* b = 21.3 m/s
* c = magnitude of the initial velocity
3. Substitute and solve:
* (18.2 m/s)² + (21.3 m/s)² = c²
* 331.24 m²/s² + 453.69 m²/s² = c²
* 784.93 m²/s² = c²
* c = √784.93 m²/s² ≈ 28.02 m/s
Answer
The magnitude of the initial velocity of the tennis ball is approximately 28.02 m/s.
