A particle is released from height S above Earth's surface. At some height h its kinetic energy equals three times its gravitational potential energy (zero at ground). Find h and speed v.
Options

Question

A particle is released from height S above Earth's surface. At some height h its kinetic energy equals three times its gravitational potential energy (zero at ground). Find h and speed v.

G1 Physics · Accepted Answer

Step 1 — Principle: For motion under gravity without resistance, total mechanical energy K + U remains constant. Step 2 — Working: Total energy is mgS. Step 3 — Working: At the instant K=3U=3mgh, so mgS=4mgh and h=S/4. Step 4 — Working: K=mg(S−h)=3mgS/4=½mv², so v=√(3gS/2). Correct answer: B — S/4 and √(3gS/2).