A(n) 0.34 kg soccer ball approaches a player horizontally with a speed of 6.18 m/s. The player illegally strikes the ball with her hand and causes it to move in the opposite direction with a speed of 31.3 m/s .

Question

A(n) 0.34 kg soccer ball approaches a player horizontally with a speed of 6.18 m/s. The player illegally strikes the ball with her hand and causes it to move in the opposite direction with a speed of 31.3 m/s .

What is the magnitude of the impulse de- livered to the ball by the player?

Answer 1

some strike...

impulse = change in momentum

i = .34 kg (31.3 m/s - -6.18 m/s)

Answer 2

To find the magnitude of the impulse delivered to the ball by the player, we can use the impulse-momentum theorem.

The impulse-momentum theorem states that the impulse delivered to an object is equal to the change in momentum of the object. Mathematically, it can be expressed as:

Impulse = Change in Momentum

Momentum is given by the product of an object's mass and its velocity. Mathematically, it can be expressed as:

Momentum = Mass x Velocity

Since we are given the mass of the soccer ball and its initial and final velocities, we can calculate the momentum before and after the player strikes the ball.

The initial momentum (before the player strikes the ball) can be calculated as:

Initial momentum = Mass x Initial velocity

Final momentum (after the player strikes the ball) can be calculated as:

Final momentum = Mass x Final velocity

To find the change in momentum, we subtract the initial momentum from the final momentum:

Change in momentum = Final momentum - Initial momentum

Finally, we can find the magnitude of the impulse by taking the absolute value of the change in momentum:

Magnitude of impulse = |Change in momentum|

Let's calculate these values with the given information:

Mass of the soccer ball (m) = 0.34 kg
Initial velocity (v1) = 6.18 m/s
Final velocity (v2) = -31.3 m/s (opposite direction)

Initial momentum = 0.34 kg x 6.18 m/s
Final momentum = 0.34 kg x (-31.3 m/s)

Change in momentum = Final momentum - Initial momentum
Magnitude of impulse = |Change in momentum|

Now let's substitute the values into the formulas and calculate the magnitude of the impulse:

Initial momentum = 0.34 kg x 6.18 m/s = 2.1092 kg·m/s
Final momentum = 0.34 kg x (-31.3 m/s) = -10.642 kg·m/s

Change in momentum = (-10.642 kg·m/s) - (2.1092 kg·m/s) = -12.7512 kg·m/s

Magnitude of impulse = | -12.7512 kg·m/s |

Taking the absolute value, the magnitude of the impulse delivered to the ball by the player is approximately 12.7512 kg·m/s.