To keep homerun records and distances consistent from year to year, organized baseball randomly checks the coefficient of restitution between new baseball and wooden surface similar to that of of an average bat. Suppose you are in charge of making sure that no "juiced" baseballs are produced.(a) In a random test, you find one that when dropped from 2.0 m rebound 0.25 m.what is the coefficient of restitution for this ball?(b) what is the maximum distance home run shot you would expect from this ball, neglecting any effect due to air resistance and making reasonable assumption for bat speeds and incoming pitch speeds? Is this a "Juiced" ball,a "normal" ball, or a "dead" ball?

Question

To keep homerun records and distances consistent from year to year, organized baseball randomly checks the coefficient of restitution between new baseball and wooden surface similar to that of of an average bat. Suppose you are in charge of making sure that no "juiced" baseballs are produced.(a) In a random test, you find one that when dropped from 2.0 m rebound 0.25 m.what is the coefficient of restitution for this ball?(b) what is the maximum distance home run shot you would expect from this ball, neglecting any effect due to air resistance and making reasonable assumption for bat speeds and incoming pitch speeds? Is this a "Juiced" ball,a "normal" ball, or a "dead" ball?

its looking for coefficient and maximum distance?

Answer 1

(a) The coefficient of restitution (COR) is a measure of how elastic a collision is between two objects. For a ball dropping and rebounding, the COR is calculated as the ratio of the rebound height to the drop height.

In this case, the ball is dropped from a height of 2.0 m and rebounds to a height of 0.25 m. Using the formula: COR = rebound height / drop height, we can calculate the COR.

COR = 0.25 m / 2.0 m = 0.125

Therefore, the coefficient of restitution for this ball is 0.125.

(b) To calculate the maximum distance a home run shot would travel, we can use the principle of conservation of energy. Neglecting air resistance, the potential energy at the highest point of the ball's trajectory will equal the kinetic energy at the point of contact with the bat.

Assuming reasonable assumptions for bat speeds and incoming pitch speeds, we can estimate the initial velocity of the ball after contact with the bat.

Let's say the bat speed is 30 m/s and the incoming pitch speed is 40 m/s.

Using the principle of conservation of energy, we can equate the potential energy at the highest point to the kinetic energy at contact:

mgh = (1/2)mv^2

Where m is the mass of the ball, g is the acceleration due to gravity, h is the height at the highest point (negligible for home runs), and v is the velocity of the ball at contact.

Simplifying the equation gives:

gh = (1/2)v^2

Substituting the known values for g and assuming a height h of zero:

(9.8 m/s^2)(0) = (1/2)v^2

Solving for v:

v = 0 m/s

Since the velocity of the ball at contact is zero, the maximum distance a home run shot would travel is zero. This indicates that the ball is a "dead" ball and does not possess a significant COR. It is not "juiced" or "normal" in terms of its bounciness.