Question

A player bounces a 0.49-kg soccer ball off her head, changing the velocity of the ball from v����� i = (8.6 m/s )x^ ( -2.6 m/s )y���o v����� f = (5.8 m/s )x^ (3.3 m/s )y^ . What is the change in velocity of the ball?

1) 2.8 m/s
2) 3.7 m/s
3) 4.8 m/s
4) 5.9 m/s

Answer 1

The total change in velocity of the soccer ball is calculated using the changes in the x and y components, resulting in an approximate value of 6.53 m/s, which is not listed in the options provided.

Step-by-step explanation:

The change in velocity of the soccer ball can be determined by subtracting the initial velocity vector from the final velocity vector. This requires calculating the change in each component (x and y) separately and then using the Pythagorean theorem to find the magnitude of the resulting vector.

The initial velocity components are v_i_x = 8.6 m/s and v_i_y = -2.6 m/s. The final velocity components are v_f_x = 5.8 m/s and v_f_y = 3.3 m/s. The changes in the x and y components are Δv_x = v_f_x - v_i_x = 5.8 m/s - 8.6 m/s = -2.8 m/s (a decrease), and Δv_y = v_f_y - v_i_y = 3.3 m/s - (-2.6 m/s) = 5.9 m/s (an increase).

To find the total change in velocity, we calculate the magnitude of the change in velocity vector: Δv = √(Δv_x^2 + Δv_y^2) = √((-2.8 m/s)^2 + (5.9 m/s)^2) = √(7.84 + 34.81) = √(42.65) ≈ 6.53 m/s. Therefore, the correct answer is not listed in the options provided.

Answer 2

The change in velocity of the soccer ball is approximately 6.5 m/s. Thus, there is no correct option,

Step-by-step explanation:

The change in velocity of the ball can be found by calculating the vector difference between the final velocity vf and the initial velocity vi. The initial and final velocities are given by vi = (8.6 m/s, -2.6 m/s) and vf = (5.8 m/s, 3.3 m/s). By subtracting the initial velocity components from the final velocity components, we can determine the change in velocity in each direction.

• The change in the x-component of velocity: Δvx = 5.8 m/s - 8.6 m/s = -2.8 m/s.
• The change in the y-component of velocity: Δvy = 3.3 m/s - (-2.6 m/s) = 5.9 m/s.

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

Δv = √(Δvx² + Δvy²)

Δv = √((-2.8 m/s)² + (5.9 m/s)²)

Δv = √(7.84 + 34.81)

Δv = √(42.65)

Δv ≈ 6.5 m/s.

Thus, there is no correct option.