Final answer:
The time of contact between the baseball and the bat, calculated using the principle of impulse and momentum conservation, is approximately 0.64 milliseconds.
Step-by-step explanation:
Calculating the Time of Contact in a Baseball Collision
To calculate the time of contact when a baseball collides with a bat, we can use the concept of impulse, which is the product of the average force exerted on an object and the time interval over which the force acts. According to the principle of conservation of momentum, the impulse is equal to the change in momentum of the baseball.
The initial velocity (vi) of the ball is 76.3 km/h, which needs to be converted to m/s:
vi = 76.3 km/h = (76.3 * 1000 m/km) / (3600 s/h) = 21.194 m/s
Since the velocity is towards the bat, we take this as negative in our calculations. The final velocity (vf) after collision is 90 km/h, which, when converted to m/s and taken as positive since it's in the opposite direction, is:
vf = 90 km/h = (90 * 1000 m/km) / (3600 s/h) = 25 m/s
The change in momentum (Δp) is calculated using the velocities and the mass (m) of the baseball:
Δp = m(vf - vi) = 0.125 kg * (25 m/s - (-21.194 m/s)) = 0.125 kg * 46.194 m/s = 5.77425 kg·m/s
To find the time of contact (t), we use the formula for impulse:
Ft = Δp
9.00 x 10³ N * t = 5.77425 kg·m/s
t = 5.77425 kg·m/s / 9.00 x 10³ N = 0.641583 ms
So, the time of contact between the baseball and the bat is approximately 0.64 milliseconds.