A body is projected with an initial velocity u at angle to the horizontal. If R max is the maximum range of…

Analyze the question: We are asked what physical quantity u²/R_max represents, where R_max is the maximum range of a projectile.

Concept: The range of a projectile launched with speed u at angle θ is

R = u² sin2θ / g

The range is greatest when sin2θ = 1, that is, when 2θ = 90°, so θ = 45°.

Solution:

At maximum range:

R_max = u² / g

Rearranging:

g = u² / R_max

So u²/R_max equals g, the acceleration due to gravity.

Checking the other options:

• A: The vertical distance covered would be something like the maximum height, H = u² sin²θ / 2g, which does not match.
• C: The horizontal distance covered is R_max itself, not u²/R_max.
• D: "The acceleration of the body" is vague. The only acceleration acting on a projectile (ignoring air resistance) is g, but option B states this precisely, so B is the better answer.

Answer: B. Acceleration due to gravity.

Exam tip: Memorize R_max = u²/g at 45°. Any question that gives you R_max and u² can be turned into g, and the same relation lets you find R_max if g is given. Also remember that H_max = u²/(4g) at 45°, so R_max = 4H_max at that angle.