How Fast Can a Cardinal Throw a Baseball?

Question:

A cardinal (Richmondena cardinalis) of mass 3.90√ó10‚àí2 kg and a baseball of mass 0.149 kg have the same kinetic energy. How fast can the cardinal throw the baseball?

Answer:

The cardinal can throw the baseball at a velocity calculated from the ratio of its momentum to that of the baseball. The momentum ratio is given by the square root of the ratio of their masses, which is √(3.90×10−2/0.149), since their kinetic energies are equal.

Explanation:

To determine how fast the cardinal can throw the baseball, we use the concepts of kinetic energy and momentum from physics. Given that the kinetic energy of both objects (the cardinal and baseball) are equal, we can calculate the velocity at which the cardinal can throw the baseball.

The kinetic energy (K) is given by the formula 1/2*mv², where m is the mass and v is the velocity. The momentum (p) is given by mv. By setting the kinetic energy equations equal to each other, we can solve for the velocity and then substitute it into the momentum equation.

Since the velocity is the same for both objects due to their equal kinetic energies, the ratio of the cardinal's momentum (pc) to the baseball's momentum (pb) can be expressed as pc/pb = √(mc/mb), where mc and mb are the masses of the cardinal and baseball respectively. Substituting the given values, we get pc/pb = √(3.90×10−2/0.149).

Therefore, the cardinal can throw the baseball at a velocity determined by the calculated ratio of momentum to that of the baseball.