A golf ball has a mass of 46 g and is initially stationary - AQA - A-Level Physics - Question 25 - 2021 - Paper 1

The impulse imparted to the golf ball is equal to the average force multiplied by the time interval during which the force acts. If we assume the time interval is roughly 10 ms (0.01 s), we can calculate the impulse:

$Impulse = F_{avg} \times \Delta t$

where ( F_{avg} \approx \rac{0.7 ext{ kN}}{2} = 0.35 ext{ kN} = 350 ext{ N} and \( \Delta t = 0.01 s, yielding

$Impulse \approx 350 ext{ N} \times 0.01 s = 3.5 ext{ N s}$.

The impulse also equals the change in momentum:

$Impulse = m \times v$ where ( m = 0.046 ext{ kg} ). Thus, we can find the final velocity ( v ):

$3.5 = 0.046 v \Rightarrow v \approx \frac{3.5}{0.046} \approx 76.09 ext{ m/s}$.

Finally, we calculate the kinetic energy (KE) of the golf ball using the formula:

$KE = \frac{1}{2}mv^2$. Substituting the values we found, we have:

$KE \approx \frac{1}{2} \times 0.046 \times (76.09)^2 \approx 107.70 ext{ J}.$
Thus, the estimated kinetic energy is closest to option C) 250 J.