Question

A particle is projected from horizontal plane $(x-y)/(z-axisisalongvertical)$ such that its velocity at time $tisV=3i+(2-4t)k$. The horizontal range of the particle is

• A. $1.5m$
• B. $3m$
• C. $6m$
• D. $9m$

Answer 1

The correct option is B $3m$

Given,

$\overrightarrow{v}=3\hat{i}+(2-4t)\hat{k}$

From the above, ${\overrightarrow{v}}_x=3m/s,{\overrightarrow{v}}_z=(2-4t)m/s$

Initial velocity at $t=0s$, $a_z=2-4\times 0=2m/s$

Acceleration, $a=\frac{dx}{dt}$

${\overrightarrow{a}}_x=0m/s^2,{\overrightarrow{a}}_z=-4m/s^2$

Along z-axis, the displacement at point $A$ is zero.

$0=u_{z}t+\frac{1}{2}{a}_z{t}^2$

$0=2t-\frac{1}{2}\left(4\right)t^2$

$2t=-2t^2$

$t=1sec$

Horizontal range, $R=v_{x}t=3\times 1$

$R=3m$