Question

A body is projected horizontally from a height with speed $20m/sec$. What will be its speed after $5sec(g=10m/s^2)$:

• A. $54m/s$
• B. $20m/s$
• C. $50m/s$
• D. $70m/s$

Answer 1

The correct option is A $54m/s$

Along x-axis,

$u_x=20m/s$

$g_x=0m/s^2$

$t=5sec$

From 1st equation of motion,

$v_x=u_x+g_{x}t$

$v_x=20+0\times 5$

$v_x=20m/s$

Along y-axis,

$u_y=0m/s$

$g_x=10m/s^2$

$t=5sec$

From 1st equation of motion,

$v_y=u_y+g_{y}t$

$v_y=0+10\times 5$

$v_y=50m/s$

Velocity of of body after $t=5sec$,

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

$\overrightarrow{v}=20\hat{i}+50\hat{j}$

The magnitude of the velocity is

$v=|\overrightarrow{v}|=\sqrt{(20{)}^2+(50{)}^2}$

$v=\sqrt{2900}m/s$

$v=53.84\approx 54m/s$

The correct option is A.