Question

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

• A. $\frac{ba}{c}$
• B. $\frac{2ba}{c}$
• C. $\frac{3ba}{c}$
• D. $\frac{ba}{2c}$

Answer 1

The correct option is B $\frac{2ba}{c}$

According to question $v_x=u_x=a$ and $v_y=u_y–gt=b–ct$
On comparing, we get
$g=c$ and $u_y=b$
We know: $R=\frac{2\left(u\sin \theta \right)\left(u\cos \theta \right)}{g}=\frac{2u_y{u}_x}{g}$
$\therefore R=\frac{2ba}{c}$