A pitcher claims he can throw a 0.157 kg baseball with as much momentum as a 1.5 g bullet moving with a speed of 1.50 multiplied by 103 m/s.
(a) What must the baseball's speed be if the pitcher's claim is valid?
m/s
(b) Which has greater kinetic energy, the ball or the bullet?
The bullet has greater kinetic energy. The ball has greater kinetic energy.
Both have the same kinetic energy.
To determine the validity of the pitcher's claim, we can compare the momentum of the baseball to that of the bullet.
The momentum is calculated using the equation:
momentum = mass × velocity
For the bullet, momentum = mass_bullet × velocity_bullet = 1.5 × 10^(-3) kg × 1.50 × 10^3 m/s = 2.25 kg·m/s
So, according to the pitcher's claim, the momentum of the baseball must also be 2.25 kg·m/s.
Using the equation for momentum, we can rearrange it to solve for the velocity of the baseball:
velocity_baseball = momentum / mass_baseball
Substituting the given values, we have:
velocity_baseball = 2.25 kg·m/s / 0.157 kg = 14.331 km/s
Therefore, according to the pitcher's claim, the speed of the baseball must be approximately 14.331 m/s.
Now, let's compare the kinetic energies of the bullet and the baseball.
The kinetic energy is given by the equation:
kinetic energy = (1/2) × mass × velocity^2
For the bullet, kinetic energy_bullet = (1/2) × 1.5 × 10^(-3) kg × (1.50 × 10^3 m/s)^2 = 1.688 J
For the baseball, using the speed we calculated earlier, the kinetic energy_baseball = (1/2) × 0.157 kg × (14.331 m/s)^2 = 15.21 J
Therefore, the baseball has a greater kinetic energy than the bullet.