Question

A body of mass $5kg$ starts from the origin with an initial velocity ${\overrightarrow{v}}_0$ = $(30\hat{i}+40\hat{j})m/s$. If a constant force $\overrightarrow{F}=-(\hat{i}+5\hat{j})N$ acts on the body, the time in which the Y-component of the velocity becomes zero is:

• A. $5s$
• B. $20s$
• C. $40s$
• D. $80s$

Answer 1

The correct option is C $40s$

Given that,

$m=5kg$

$u={\overrightarrow{v}}_0=30\hat{i}+40\hat{j}m/s$

Hence, $u_y=40m/s$

$F=–(\hat{i}+5\hat{j})N$

Hence $F_y=–5N$

From second law of motion we get:-

$F=ma⟹a=(\frac{F}{m})$

$⟹a_y=(\frac{F_y}{m})=\frac{–5}{5}$

$⟹a_y=–1m/s^2$

From equation of motion we get:-

$v_y=u_y+at$
At time $t$, velocity $v_y$ becomes zero

$⟹0=u_y+at$

$⟹u_y=–at$
$⟹t=\frac{-40}{-1}=40secs$