Question

A particle is dropped from the top of a tower. It covers 40m in last 2s. Find the height of the tower.

Answer 1

Let h = the height of the tower that needs to be determined.

Let t be the time of fall.

Then (t - 2) would be the time to reach the top of the 40 meter mark, and let d be the distance fallen till it reaches the 40 m mark.

Using kinematics, we can write:

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

And $H=1/2g{t}^2$

H also $=40+d$

Then: $H=40+1/2g(t-2{)}^2=1/2g{t}^2$

$40+5t^2-20t+20=5t^2$

$t=3s$

$(t-2)=1second$

In one second an object falls 5 m

Then $H=45m$