A golf club with 65 J of kinetic energy strikes a stationary golf ball with a mass of 46g. The energy transfer is only 20% efficient. Calculate the initial speed of the golf ball.
First, we need to convert the mass of the golf ball from grams to kilograms:
46g = 0.046kg
Next, we can calculate the total energy transferred from the golf club to the golf ball using the efficiency:
Total energy transferred = 65 J / 20% = 65 J / 0.2 = 325 J
We know that the total energy transferred is equal to the initial kinetic energy of the golf ball:
Kinetic energy = 0.5 * mass * velocity^2
Rearranging the equation, we can solve for the velocity:
Velocity = sqrt((2 * kinetic energy) / mass)
Plugging in the values, we have:
Velocity = sqrt((2 * 325 J) / 0.046kg)
Velocity = sqrt(14130.43)
Velocity ≈ 118.91 m/s
Therefore, the initial speed of the golf ball is approximately 118.91 m/s.