Question

A pitcher claims he can throw a 0.147-kg baseball with as much momentum as a 3.50-g bullet moving with a speed of 1.50 ✕ 103 m/s. What must the baseball's speed be if the pitcher's claim is valid? Which has greater kinetic energy, the ball or the bullet?

Answer 1

The speed of the baseball must be 35.8 m/s for the pitcher's claim to be valid. The bullet has a greater kinetic energy than the baseball.

Step-by-step explanation:

To determine the speed of the baseball, we need to use the principle of conservation of momentum which states that the total momentum before an event is equal to the total momentum after the event. Since momentum is given by p = mv, where p is momentum, m is mass, and v is velocity, we can set up the following equation:

(mass of bullet) x (velocity of bullet) = (mass of baseball) x (velocity of baseball)

Solving for the velocity of the baseball:

velocity of baseball = [(mass of bullet) x (velocity of bullet)] / (mass of baseball)

Substituting the given values:

velocity of baseball = [(0.00350 kg) x (1500 m/s)] / (0.147 kg) = 35.8 m/s

The kinetic energy of an object is given by the equation KE = 0.5mv². Using this equation, we can compare the kinetic energy of the baseball and the bullet:

Kinetic energy of the baseball = 0.5 x (0.147 kg) x (35.8 m/s)²

Kinetic energy of the bullet = 0.5 x (0.00350 kg) x (1500 m/s)²

Calculating the kinetic energies:

Kinetic energy of the baseball = 94.5 J

Kinetic energy of the bullet = 3937.5 J

Therefore, the bullet has a greater kinetic energy than the baseball.