An object is moving with a velocity of 5m-1. At what height must a similar body be situated to have a…

Analyze the question: A body moves at 5 m/s (the "5m-1" is a typo for 5 m s⁻¹). We need the height at which a similar body (same mass) has potential energy equal to the kinetic energy of the moving body.

Concept:

• Kinetic energy: KE = ½mv²
• Potential energy: PE = mgh

Solution:

Set PE = KE:

mgh = ½mv²

The mass cancels because the bodies are similar:

gh = ½v²

h = v² / (2g)

Take g = 10 m/s²:

h = (5)² / (2 × 10) = 25 / 20 = 1.25 m ≈ 1.3 m

If g = 9.8 m/s², h = 25 / 19.6 ≈ 1.28 m, which also rounds to 1.3 m.

Answer: The height is about 1.3 m, which is option C.

Tip: When KE and PE are equated for the same mass, the mass always cancels, so use h = v²/2g directly. Be careful not to forget the ½. Forgetting it gives h = v²/g = 2.5 m, which is not an option. Options like 25 m come from forgetting to divide by g.