Question

The horizontal range and maximum height attained by a projectile are R and H respectively. If a constant horizontal acceleration a = g/4 is imparted to the projectile due to wind, then its horizontal range and maximum height will be

• A. $\left(\text{R}+\text{H}\right)\text{, }\frac{\text{H}}{2}$
• B. $\left(\text{R}+\frac{\text{H}}{2}\right)\text{, }2\text{H}$
• C. (R + 2H), H
• D. (R + H), H

Answer 1

Answer: (D)

$\text{T}=\frac{2{\text{u}}_{\text{y}}}{\text{g}}\text{, }\text{H}=\frac{{\text{u}}_{\text{y}}^2}{2\text{g}}$
where T = time of flight of the projectile and u_x and u_y are respectively the horizontal and vertical components of initial velocity
When a horizontal acceleration is also given to the projectile u_y and hence T and H will remain unchanged while the range will become
$\text{R}={\text{u}}_{\text{x}}\text{T}+\frac{1}{2}{\text{aT}}^2$
$=\mathrm{R}+\frac{1}{2}\left(\frac{\mathrm{g}}{4}\right)\left(\frac{4{\mathrm{u}}_{\mathrm{y}}^2}{{\mathrm{g}}^2}\right)$
= R + H