Question

A player bounces a 0.48-kg soccer ball off her head, changing the velocity of the ball from v⃗ i = (8.1 m/s )x^ ( -2.1 m/s )y^ to v⃗ f = (5.6 m/s )x^ (4.0 m/s )y^ . What is the change in velocity of the ball?

1) 2.5 m/s
2) 3.5 m/s
3) 4.5 m/s
4) 5.5 m/s

Answer 1

The correct magnitude of the change in velocity of the soccer ball should be approximately 6.6 m/s, which was calculated using the vector difference between the final and initial velocities, and none of the provided options are correct.

Step-by-step explanation:

The change in velocity of the soccer ball can be found by calculating the vector difference between the final velocity, v_f, and the initial velocity, v_i. We can do this by subtracting the components of the initial velocity from the final velocity.

Change in velocity (Δv) in the x-direction = v_fx - v_ix = 5.6 m/s - 8.1 m/s = -2.5 m/s
Change in velocity (Δv) in the y-direction = v_fy - v_iy = 4.0 m/s - (-2.1 m/s) = 6.1 m/s

The magnitude of the change in velocity can be found using the Pythagorean theorem:

|Δv| = √((Δvx)² + (Δvy)²)
|Δv| = √((-2.5 m/s)² + (6.1 m/s)²)
|Δv| = √(6.25 + 37.21) m²/s²
|Δv| = √(43.46) m²/s²
|Δv| ≈ 6.6 m/s

Therefore, none of the provided options (2.5 m/s, 3.5 m/s, 4.5 m/s, 5.5 m/s) are correct for the change in velocity of the soccer ball, as the correct answer is approximately 6.6 m/s.