Question

The height $y$ and horizontal distance $x$ covered by a projectile in a time $t$ seconds are given by the equations $y=8t-5t^2$ and $x=6t$. If $x$ and $y$ are measured in meters, the velocity of projection is:-

• A. $10m{s}^{-1}$
• B. $6m{s}^{-1}$
• C. $8m{s}^{-1}$
• D. $14m{s}^{-1}$

Answer 1

The correct option is A $10m{s}^{-1}$

$v_x=\frac{dx}{dt}=6$

$v_y=\frac{dy}{dt}=8-10t$

$\overrightarrow{v}=v_x\hat{i}+v_y\hat{j}$

$\overrightarrow{u}={\overrightarrow{v}}_{t=0}$

$\overrightarrow{u}=6\hat{i}+8\hat{j}$

$u=\sqrt{6^2+8^2}$

$u=10m/s$