Question

A charged object of mass $1kg$ is projected at $t=0$ from ground with a velocity of $10\sqrt{2}m/s$ making an angle ${45}^o$ with horizontal. In the entire region, an electric field is applied at $t=0$, due to which a time varying force $F=12tN$, where $t$ is in seconds acts on the object in horizontally forward direction. At how much distance from the starting point, the object strikes the ground? ($g=10m/s^2$)

• A. $10m$
• B. $48m$
• C. $68m$
• D. $20m$

Answer 1

The correct option is C $68m$

Since, electrical force is acting in horizontal direction. time of flight does not change.

$T=2u\sin \theta /g$

Along horizontal direction,

$F=12t=ma$

$⟹a=12t\because m=1$

Using second equation of motion,

$s=u\cos \theta t+1/2a{t}^2$

$s=u\cos \theta t+6t^3$

$s=\frac{2u^2\sin \theta \cos \theta }{g}+\frac{48u^3{\sin }^3\theta }{g^3}$

$s=20+48=68m$