A 0.34 kg soccer ball approaches a player horizontally with a velocity of 19 m/s to the north. The player strikes the ball and causes it to move in the opposite direction with a velocity of 22 m/s.
What impulse was delivered to the ball by the player? Answer in units of kg · m/s.
The change in momentum is
(vf-vi )m
(22- -19)m=m*41
To find the impulse delivered to the ball by the player, you can use the concept of momentum. Impulse is defined as the change in momentum, which is equal to the mass of the object multiplied by the change in velocity.
Given:
Mass of the soccer ball (m) = 0.34 kg
Initial velocity of the soccer ball (v_initial) = 19 m/s to the north
Final velocity of the soccer ball (v_final) = -22 m/s (opposite direction)
To find the impulse, we need to calculate the change in momentum (Δp):
Δp = m * Δv
First, find the change in velocity (Δv):
Δv = v_final - v_initial
Δv = -22 m/s - 19 m/s
Δv = -41 m/s
Next, calculate the impulse:
Impulse = Δp = m * Δv
Impulse = 0.34 kg * (-41 m/s)
Impulse = -13.94 kg·m/s
Therefore, the impulse delivered to the ball by the player is -13.94 kg·m/s.
To find the impulse delivered to the ball by the player, we can use the principle of impulse-momentum. The impulse (J) is equal to the change in momentum (Δp) of the ball.
The formula for impulse is:
J = Δp
The momentum of an object is given by the product of its mass (m) and its velocity (v). So, we can write the change in momentum as:
Δp = m * vf - m * vi
Where:
- Δp is the change in momentum
- m is the mass of the object
- vf is the final velocity of the object
- vi is the initial velocity of the object
Given:
- m = 0.34 kg (mass of the soccer ball)
- vf = -22 m/s (final velocity of the ball)
- vi = 19 m/s (initial velocity of the ball)
Substituting the given values into the formula, we have:
Δp = (0.34 kg * -22 m/s) - (0.34 kg * 19 m/s)
Simplifying the equation:
Δp = (-7.48 kg·m/s) - (6.46 kg·m/s)
Δp = -13.94 kg·m/s
Therefore, the impulse delivered to the ball by the player is -13.94 kg·m/s. The negative sign indicates a change in direction of the momentum.