Question

A particle is projected from a horizontal plane (x-y plane) such that its velocity vector at time t is given by $v=a\hat{i}+(b-ct)\hat{j}$. Its range on the horizontal plane is given by

• A. $\frac{2ab}{c}$
• B. $\frac{2ac}{b}$
• C. $\frac{ac}{b}$
• D. $\frac{a}{2bc}$

Answer 1

The correct option is A $\frac{2ab}{c}$

When the particle reaches the maximum position in y direction is, $v_y=0$
$\Rightarrow b-ct=0$
$\Rightarrow t=\frac{b}{c}$
Time of flight is twice the time taken to reach the maximum position in y direction. Therefore, the time of flight is $2\frac{b}{c}$.
Range is the distance travelled in x direction during the time of flight. So
Range $=v_x\times \text{Time of flight}=\frac{2ab}{c}$