Question

An arrow shot vertically upwards loses its initial speed by $60\%$ in $3$ seconds. The maximum height reached by the arrow is? $(g=9.8m{s}^{-2})$

• A. $122.5$ m
• B. $44.1$ m
• C. $100$ m
• D. $45$ m

Answer 1

The correct option is A $122.5$ m

Let the initial speed be $u$ ,, so after 3 sec it speed will be $\frac{2}{5}u$
so from first equation of motion

$v=u+at$

$\frac{2}{5}u=u-9.8\times 3$

$u=9.8\times 3\times \frac{5}{3}=49\frac{m}{s}$

$u=49\frac{m}{s}$

Now third equation of motion

$v^2=u^2+2as$

at maximum height $V=0,$

So$H=\frac{u^2}{2}g$

$H=49\times \frac{49}{2}\times 9.8$

$H=122.5m$