Free fall from height h – find the impact speed at ground Neglecting air resistance, a body is dropped from rest from a height h above level ground. What is the correct expression for its speed v just before impact?

Introduction / Context:
Impact speed from free fall is a fundamental kinematics result used across engineering—estimating drop tests, safety barriers, and potential energy conversion. It follows from constant-acceleration motion under gravity without air drag.

Given Data / Assumptions:

• Initial velocity u = 0 from height h.
• Constant acceleration a = g downward.
• No air resistance; motion is vertical.

Concept / Approach:

Use the kinematic energy–speed relation or the third equation of motion. Either approach removes time and relates velocity directly to displacement under constant acceleration.

Step-by-Step Solution:

Verification / Alternative check:

Dimensions: g has L/T^2 and h has L; 2 g h has L^2/T^2; its square root has L/T, the correct unit of speed.

Why Other Options Are Wrong:

(b) and (d) are missing the square root and have wrong units. (c) inverts the relationship. (e) has incorrect dependence on h and g.

Common Pitfalls:

Forgetting the square root; using time-dependent formulas unnecessarily; sign mistakes when taking displacement as negative.

Final Answer:

v = sqrt(2 g h)