How to Calculate the Initial Speed and Angle of a Projectile

What are the initial horizontal and vertical velocities of a soccer ball?

The initial horizontal velocity of the soccer ball is 18 m/s and the initial vertical velocity is 21 m/s. What is the initial speed of the ball based on these velocities?

Initial Speed Calculation

The initial speed of the ball is the combination of its horizontal and vertical velocities. To find the initial speed, you can use the Pythagorean theorem:

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the horizontal velocity (18 m/s) and vertical velocity (21 m/s) of the soccer ball can be considered as the two sides of a right triangle.

Using the Pythagorean theorem formula:

Initial speed = √(horizontal velocity^2 + vertical velocity^2)

Substitute the given values:

Initial speed = √(18^2 + 21^2)

Initial speed = √(324 + 441)

Initial speed = √765

Initial speed ≈ 27.7 m/s

Therefore, the initial speed of the soccer ball is approximately 27.7 m/s.