Question

A body of mass $1\text{kg}$ is projected with velocity $50\text{m/s}$ at an angle of ${30}^{\circ }$ with the horizontal. At the highest point of its path, a force $10\text{N}$ starts acting on body for $5s$ vertically upwards besides gravitational force. What is horizontal range of the body ? ($g=10{\text{m/s}}^2$):

• A. $125\sqrt{3}\text{m}$
• B. $200\sqrt{3}\text{m}$
• C. $500\text{m}$
• D. $250\sqrt{3}\text{m}$

Answer 1

The correct option is D $250\sqrt{3}\text{m}$

Since $mg=10\text{N}$, the projectile will move with a constant speed of $u\cos \theta$ in a straight line for $5s$ once it reaches the highest point and then continues its usual parabolic motion thereafter.



Actual range $=\frac{R}{2}+u\cos \theta t_0+\frac{R}{2}$
$=R+u\cos \theta t_0$
$=\frac{u^2\sin 2\theta }{g}+u\cos \theta t_0$
$=\frac{{50}^2\times \sin {60}^{\circ }}{10}+50\times \cos {30}^{\circ }\times 5$
$=125\sqrt{3}+125\sqrt{3}$
$=250\sqrt{3}\text{m}$