## Step-by-Step Solution ### **Step 1: Identifying the Physics Concepts** The distance a golf ball travels depends on: - **Initial velocity (v₀)** - **Launch angle (θ)** - **Air resistance (drag)** - **Lift (Magnus effect, due to spin)** - **Surface texture of the ball** ### **Step 2: Relevant Formulas** #### **(A) Projectile Motion Without Air Resistance** The range \( R \) of a projectile is: \[ R = \frac{v_^2 \sin 2\theta}{g} \] where \( v_ \) = initial speed, \( \theta \) = launch angle, \( g \) = acceleration due to gravity. #### **(B) Air Resistance (Drag Force)** Drag force is: \[ F_D = \frac{1}{2} C_D \rho A v^2 \] - \( C_D \): drag coefficient (depends on surface roughness) - \( \rho \): air density - \( A \): cross-sectional area - \( v \): velocity ### **Step 3: Effect of Surface Roughness** - **Golf balls have dimples** designed to optimize drag and lift. - **Worn surfaces** (dimples smoothed out) **increase drag** (\( C_D \) increases). - **Higher drag** causes the ball to **slow down faster**, reducing range. ### **Step 4: Combining the Formulas** If the surface is worn: - \( C_D \) increases → \( F_D \) increases. - Ball loses speed faster → range \( R \) **decreases**. ### **Step 5: Conclusion** **The claim is NOT true.** Wearing down the surface of a golf ball increases drag, which **reduces the distance** the ball can travel. The special dimpled design is intentional to help the ball fly farther. --- ## **Final Answer** > **No, the claim is not true. Worn golf ball surfaces increase air resistance (drag), as shown by the drag formula \( F_D = \frac{1}{2} C_D \rho A v^2 \). A higher drag coefficient makes the ball slow down faster, so it travels a shorter distance. The dimpled design of golf balls is specifically to reduce drag and maximize range.**