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. ba/c
• B. 2ba/c
• C. 3ba/c
• D. None

Answer 1

The correct option is B

2ba/c

$\overrightarrow{v}=a\hat{i}+(b-ct)\hat{j}$
The actual velocity is given by,
$\overrightarrow{V}=u_x\hat{i}+(u_y-gt)\hat{j}$
On comparing the two equations,
u_x =a
u_y = b
g = c

$\text{Range};R=\frac{2u_x{v}_y}{g}=\frac{2ab}{c}$