Projectile motion on inclined planes: Compare the range on a downward slope versus an upward slope for identical launch parameters. Conditions: Same initial speed (u) and same launch angle (α) with respect to the horizontal; magnitude of plane inclination (|β|) is the same in both cases. Choose the correct comparative statement about the range measured along the plane.

Given data

• Same initial speed u and launch angle α for both cases.
• Same magnitude of plane inclination |β| (one case upward, the other downward).

Concept/Approach For a projectile on an inclined plane, the range along the plane is R(β) = (2u² cosα · sin(α − β)) / (g cos²β) where β is taken positive for an upward slope and negative for a downward slope.

Step-by-step reasoning Upward plane: R_up ∝ sin(α − β). Downward plane: R_down ∝ sin(α − (−β)) = sin(α + β). For 0 < β < α < 90°, we have sin(α + β) > sin(α − β). ⇒ R_down > R_up.

Common pitfall Do not compare horizontal ranges; the comparison is for range measured along the plane.

Final Answer Greater than