Question

The Petronas twin towers in Malaysia and the Chicago Sears tower have heights of about 452 m and 443 m respectively. If objects were dropped from the top of each, what would be the difference in the time it takes for the objects to reach the ground?

Answer 1

Answer:

0.09 s

Explanation:

From the second equation of motion,

$S=ut+\frac{1}{2}at^{2}$

Here, u is the initial velocity, a is the acceleration due to gravity, t is time taken, and S is the total displacement or distance.

From the given problem,

initial velocity is zero for both the case.

And the distance of twin  tower of malaysia is, $S_{1}=452m$

And the distance of Sears tower of Chicago is, $S_{1}=443m$

Now,rearrange the distance equation for t.

$t=\sqrt{\frac{2S}{a} }$

So time difference.

$\Delta t=\sqrt{\frac{2(452)}{9.8} }-\sqrt{\frac{2(443)}{9.8} }\\\Delta t=\sqrt{92.244898}-\sqrt{90.4081633}  \\\Delta t=9.60 s-9.51s\\\Delta t=0.09 s$

Therefore, the difference in time, object will reach the ground is 0.09 s