A student proposes the following expression for the vertical displacement (measured…
PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors
Problem
A student proposes the following expression for the vertical displacement y (measured upward) of a projectile fired from ground level at speed u after time t:
y=ut−2gt2+6Ru2t3
where g is the acceleration due to gravity and R is the radius of the Earth.
(i) Write the dimensional formula of each term that appears in the expression.
(ii) Verify whether the expression is dimensionally homogeneous.
(iii) If any term renders the expression dimensionally inconsistent, suggest how the expression may be modified (by inserting a suitable quantity or otherwise) to restore dimensional consistency.