Question

An object falls from the top of the tower travels 24.5 m in the last second before striking the
ground. Find the height of the tower​

Answer 1

Question :-

An object falls from the top of the tower travels 24.5 m in the last second before striking the ground. Find the height of the tower ?

Answer :-

→ Hence, the height of tower is 43.5 m

To Find :-

Find the height of tower.

Explanation :-

Let h be the height of tower,

Total time taken to reach on ground is "t",

Therefore,

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

Now,

$h \: - 24.5 = \frac{1}{2} g \: {(t - 1)}^{2} \\ \rightarrow \small \: \frac{1}{2} g \: {t}^{2} - 24.5 = \frac{1}{2} g \: ( {t}^{2} + 1 - 2t) \\ \\ \rightarrow \small 0.5 \: g \: {t}^{2} - 24.5 = 0.5\:g {t}^{2}+ 0.5g \: - 2 \times 0.5 \: g \: t \\ \\ \rightarrow \: gt \: - 24.5 = 0.5 \: g \\ \\ \: taking \: \: g \: = 10 \\ \\ \rightarrow \: 10t \: = 5 + 24.5 \\ \\ \rightarrow \: \boxed{t \: = 2.65 \: second \: }$

Now put the value of "t" in equation (1)

$\implies \: h \: = \frac{1}{2} \times 10 \times {(2.95)}^{2} \\ \\ \implies \: \boxed{ h \: = 43.5 \: m}$

Hence, the height of tower is 43.5 m