Question

A body falls freely from a tower and travels a distance of $40m$ in its last two seconds. The height of the tower is (take $g=10m/s^2)$.

• A. $54m$
• B. $45m$
• C. $80m$
• D. $65m$

Answer 1

Answer: (B)

$45m$

$\frac{1}{2}g{t}^2=h$
$\frac{1}{2}g(t-2{)}^2=h^{\prime }$
$h-h^{\prime }=\frac{1}{2}g{t}^2-\frac{1}{2}g(t-2{)}^2$
$=\frac{1}{2}g{t}^2-\frac{1}{2}g[t^2+4-4t]$
$40=\frac{1}{2}g[4t-4]$
$40=\frac{10}{2}[4t-4]$
So, $t=3s$
$h=\frac{1}{2}\times 10\times (3{)}^2$
$=45m$
Hence, option $\left(2\right)$ is correct.