Question

6.

A pitcher throws a baseball towards home plate. The baseball, which has a
mass of 145 g, approaches the plate with 122 J of kinetic energy. Calculate
the speed of the baseball. Show your work.

Answer 1

To find the baseball's speed, use the kinetic energy formula, KE = 1/2 m v^2, and rearrange to solve for v, which upon calculation with the provided mass and kinetic energy, results in a speed of approximately 41.02 m/s.

Step-by-step explanation:

To calculate the speed of the baseball, we will use the formula for kinetic energy (KE), which is KE = 1/2 m v^2, where m is the mass of the baseball and v is its velocity. We are given that the mass (m) of the baseball is 145 g (which we will convert to kilograms by dividing by 1000 to get 0.145 kg), and the kinetic energy (KE) is 122 Joules.

To find the velocity (v), we rearrange the kinetic energy equation to solve for v: v = sqrt(2 * KE / m).

Step-by-step calculation:

1. Convert the mass of the baseball to kilograms: m = 145 g / 1000 = 0.145 kg.
2. Plugging the mass and kinetic energy into the velocity equation: v = sqrt(2 * 122 J / 0.145 kg).
3. Calculate the velocity: v ≈ sqrt(1682.76) ≈ 41.02 m/s.

The velocity of the baseball is approximately 41.02 meters per second when it approaches the plate.