A baseball player hits a baseball (m = 0.145 kg) The ball is initially traveling horizontally with speed of 36 m/s. The batter hits a fly ball as shown, with a speed vf = 54 m/s.

(a) What is the magnitude and direction of the impulse imparted to the ball?

(b) If the ball (m = 0.145 kg) and bat are in contact for a time of 8.4 ms, what is the magnitude of the average force of the bat on the ball?

Compare this answer to the weight of the ball.
The contact force is 4 times the ball's weight.

(c) What is the impulse imparted to the bat?

To solve this question, we can use the concepts of impulse and momentum.

(a) To find the magnitude and direction of the impulse imparted to the ball, we can use the equation:

Impulse = Change in Momentum

Momentum (p) is given by the product of mass and velocity: p = m * v

The initial momentum of the ball is p_initial = m * v_initial = 0.145 kg * 36 m/s = 5.22 kg·m/s

The final momentum of the ball is p_final = m * v_final = 0.145 kg * 54 m/s = 7.83 kg·m/s

Therefore, the change in momentum is Δp = p_final - p_initial = 7.83 kg·m/s - 5.22 kg·m/s = 2.61 kg·m/s

The magnitude of the impulse imparted to the ball is the absolute value of the change in momentum: |Δp| = |2.61 kg·m/s| = 2.61 kg·m/s

The direction of the impulse is the same as the direction of the change in momentum, which in this case is in the direction of the final velocity of the ball.

(b) To find the magnitude of the average force of the bat on the ball, we can use the equation:

Impulse = Force * Time

Rearranging the equation, we have:

Force = Impulse / Time

The impulse is given in part (a) as 2.61 kg·m/s, and the time is given as 8.4 ms, which is equal to 0.0084 s.

Therefore, the magnitude of the average force is:

Force = 2.61 kg·m/s / 0.0084 s = 310.71 N

Comparing this answer to the weight of the ball (mg = 0.145 kg * 9.8 m/s^2 = 1.421 kg·m/s^2), we find that the contact force is approximately 4 times the weight of the ball.

(c) To find the impulse imparted to the bat, we can use the same equation as in part (a):

Impulse = Change in Momentum

Since the bat is initially at rest, its initial momentum is zero. The final momentum of the bat is equal in magnitude but opposite in direction to the final momentum of the ball, as momentum is conserved in this collision.

Therefore, the impulse imparted to the bat is equal to the magnitude of the change in momentum of the ball:

Impulse = Δp = 2.61 kg·m/s

So, the impulse imparted to the bat is 2.61 kg·m/s.

To determine the answers to these questions, we need to use the principles of impulse and momentum. Impulse can be defined as the change in momentum of an object, and it is equal to the force applied to the object multiplied by the time it acts upon it.

(a) To calculate the impulse imparted to the ball, we need to know the change in momentum. The initial momentum of the ball is given by the product of its mass and initial velocity, and the final momentum is given by the product of its mass and final velocity. The change in momentum is then the final momentum minus the initial momentum.

Initial momentum (Pi) = mass x initial velocity
Pi = 0.145 kg x 36 m/s
Pi = 5.22 kg·m/s

Final momentum (Pf) = mass x final velocity
Pf = 0.145 kg x 54 m/s
Pf = 7.83 kg·m/s

Change in momentum (ΔP) = Pf - Pi
ΔP = 7.83 kg·m/s - 5.22 kg·m/s
ΔP = 2.61 kg·m/s

The magnitude of the impulse imparted to the ball is the magnitude of the change in momentum, which is 2.61 kg·m/s. The direction of the impulse is the same as the direction of the change in momentum, which in this case, would be in the same direction as the final velocity of the ball.

(b) To determine the magnitude of the average force of the bat on the ball, we can use the formula for impulse: force multiplied by the time of contact.

Average force (F) = impulse / time of contact
F = ΔP / t

Given that the time of contact is 8.4 ms, we need to convert it to seconds by dividing by 1000: 8.4 ms / 1000 = 0.0084 s.

F = 2.61 kg·m/s / 0.0084 s
F ≈ 310.71 N

Therefore, the magnitude of the average force of the bat on the ball is approximately 310.71 Newtons.

To compare this answer to the weight of the ball, we can calculate the weight of the ball using the formula: weight = mass x gravitational acceleration.

Weight = 0.145 kg x 9.8 m/s²
Weight ≈ 1.42 N

The contact force (average force) of the bat on the ball is approximately 310.71 N, which is nearly 4 times greater than the weight of the ball.

(c) To calculate the impulse imparted to the bat, we can use the fact that the impulse imparted to the bat is equal in magnitude but opposite in direction to the impulse imparted to the ball.

Impulse imparted to the bat = -ΔP (negative because it is in opposite direction)
Impulse imparted to the bat = -2.61 kg·m/s

Therefore, the impulse imparted to the bat is -2.61 kg·m/s.

hellloooooo