Soccer Ball Initial Speed Calculation

What is the initial speed of the ball?

The initial speed of the ball is approximately 25.5 m/s. To find the initial speed of the ball, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the horizontal and vertical velocities of the ball form the two sides of a right triangle, and the initial speed of the ball is the hypotenuse. So, using the Pythagorean theorem, we have:
initial speed = √(horizontal velocity² + vertical velocity²)
initial speed = √(17² + 19²)
initial speed = √(289 + 361)
initial speed = √650
initial speed ≈ 25.5 m/s

Final answer:

The initial speed of the ball can be found using the vector sum of the horizontal and vertical velocities. Using the Pythagorean theorem, the initial speed is calculated to be 25.5 m/s.

Explanation:

The initial speed of the ball can be found using the vector sum of the horizontal and vertical velocities. We can use the Pythagorean theorem to calculate the magnitude of the initial speed:
s = √(vx² + vy²)
Where vx is the horizontal velocity (17 m/s) and vy is the vertical velocity (19 m/s). Plugging in the values, we get:
s = √((17 m/s)² + (19 m/s)²)
s = √(289 m²/s² + 361 m²/s²)
s = √650 m²/s²
s = 25.5 m/s

1) What is the initial speed of the ball?

The initial speed of the ball is approximately 25.5 m/s.

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