A ball of mass m is projected at angle θ with a horizontal tailwind producing constant horizontal force mg/√3. If the maximum horizontal range occurs at θ = 15°k, determine k.
Physics · Mixed Chapter
JEE Main Practice

Question

A ball of mass m is projected at angle θ with a horizontal tailwind producing constant horizontal force mg/√3. If the maximum horizontal range occurs at θ = 15°k, determine k.

G1 Physics · Accepted Answer

Step 1 — Vertical motion unaffected by horizontal wind: time of flight T = 2u sinθ/g. Step 2 — Horizontal acceleration from wind is aₓ = (mg/√3)/m = g/√3. Step 3 — Range R = (u cosθ)T + (1/2)aₓT² = (u²/g)[sin2θ + (2/√3)sin²θ]. Step 4 — Differentiate: dR/dθ ∝ 2 cos2θ + (2/√3)sin2θ = 0. For maximum range tan2θ = −√3 and 2θ = 120°, so θ = 60°. Step 5 — θ = 15°k ⇒ k = 60/15 = 4.