A golf ball hits a wall and bounces back at \( 3 / 4 \) the original speed. What part of the original kinetic energy of the ball did it lose in the collision? 1) \( 1 / 4 \) 2) \( 3 / 8 \) 3) \( 7 / 16 \) 4) \( 9 / 16 \) 5) \( 11 / 16 \)

To find out how much kinetic energy the golf ball loses during the collision, we can use the formula for kinetic energy, which is \( KE = \frac{1}{2} m v^2 \). Let the initial speed of the ball be \( v \). The initial kinetic energy (\( KE_{initial} \)) is: \[ KE_{initial} = \frac{1}{2} m v^2 \] After hitting the wall, the speed of the ball is \( \frac{3}{4}v \). The final kinetic energy (\( KE_{final} \)) is: \[ KE_{final} = \frac{1}{2} m \left( \frac{3}{4}v \right)^2 = \frac{1}{2} m \cdot \frac{9}{16} v^2 = \frac{9}{32} mv^2 \] Now, to find the kinetic energy lost during the collision, we can subtract \( KE_{final} \) from \( KE_{initial} \): \[ \text{Energy Lost} = KE_{initial} - KE_{final} = \frac{1}{2} mv^2 - \frac{9}{32} mv^2 \] Converting \( \frac{1}{2} \) to a fraction with a denominator of 32: \[ \frac{1}{2} = \frac{16}{32} \] Now, we can calculate the energy lost: \[ \text{Energy Lost} = \frac{16}{32} mv^2 - \frac{9}{32} mv^2 = \frac{7}{32} mv^2 \] To find the proportion of kinetic energy lost compared to the initial energy, we divide the energy lost by the initial energy: \[ \text{Proportion Lost} = \frac{\frac{7}{32} mv^2}{\frac{16}{32} mv^2} = \frac{7}{16} \] So the golf ball loses \( \frac{7}{16} \) of its original kinetic energy in the collision. The correct answer is: 3) \( 7 / 16 \)