Question

Plz solve Q. 14 problem in the attachment.

Answer 1

Question :

A coin is dropped from a tower. It moves through a distance of 24.5m in the last second before hitting the ground. Find the height of the tower.

Solution :

Let time taken by coin to reach at the ground be t and height of the tower be H.

So we can say that,

$\sf:\implies\:H=\dfrac{1}{2}gt^2$

$\sf:\implies\:t=\sqrt{\dfrac{2H}{g}}$

Distance covered by coin in the last second is 24.5 m.

$\sf:\implies\:S_t-S_{(t-1)}=24.5$

$\sf:\implies\:\left[\dfrac{1}{2}gt^2\right]-\left[\dfrac{1}{2}g(t-1)^2\right]=24.5$

$\sf:\implies\:gt-\dfrac{g}{2}=24.5$

$\sf:\implies\:g\left(t-\dfrac{1}{2}\right)=24.5$

$\sf:\implies\:\sqrt{\dfrac{2H}{g}}-\dfrac{1}{2}=\dfrac{24.5}{9.8}$

$\sf:\implies\:\sqrt{\dfrac{2H}{g}}=(2.5+0.5)$

$\sf:\implies\:\dfrac{2H}{g}=3^2$

$\sf:\implies\:H=\dfrac{9\times9.8}{2}$

$:\implies\:\underline{\boxed{\bf{\orange{H=44.1\:m}}}}$