A ball is thrown vertically downward from height 20 m with initial speed v₀. On impact it loses 50% of its energy and rebounds to the original height. Find v₀; take g=10 m s⁻².
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A ball is thrown vertically downward from height 20 m with initial speed v₀. On impact it loses 50% of its energy and rebounds to the original height. Find v₀; take g=10 m s⁻².

G1 Physics · Accepted Answer

Step 1 — Principle: A short collision conserves linear momentum, whereas kinetic energy may be lost to other forms. Step 2 — Working: Rebound to 20 m requires rebound KE=mg×20, exactly half KE before collision. Step 3 — Working: Thus KE before collision=40mg, so impact speed squared=80g. Step 4 — Working: From fall v²=v₀²+2g×20, giving v₀²=40g=400 and v₀=20 m/s. Correct answer: B — 20 m s⁻¹.