The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. What will the percentage increase in the horizontal range?

As maximum height,

H = (u² sin²θ) / (2g)     ...(i)

Let ΔH be the increase in H when u changes by Δu. Differentiating (i), we get:

ΔH / H = 2Δu / u

Given that the percentage increase in H is 10%,

ΔH / H = 10 / 100 = 0.1 ⇒ 2Δu / u = 0.1

As R = (u² sin2θ) / g,

ΔR / R = 2Δu / u = 0.1

∴ Percentage increase in horizontal range = (ΔR / R) × 100 = 0.1 × 100 = 10%