Question

A stone is dropped from the top of a tower and travels $24.5m$ in the last second of its journey. The height of the tower is :

• A. $44.1m$
• B. $49m$
• C. $78.4m$
• D. $72m$

Answer 1

Answer: (A)

$44.1m$

Let the total height of the tower is $h$ and the total time is taken to reach the ground is $t$.

The height is given as,

$h=\frac{1}{2}g{t}^2$ (1)

The height before last seconds is given as,

$h-24.5=\frac{1}{2}g{\left(t-1\right)}^2$

$\frac{1}{2}g{t}^2-24.5=\frac{1}{2}g{\left(t\right)}^2+\frac{1}{2}g-gt$

$t=3s$

Substitute the value of $t$ in the equation (1), we get

$h=\frac{1}{2}\times 9.8{\left(3\right)}^2$

$h=44.1m$

Thus, the height of the tower is $44.1m$.