Question

A body dropped from the top of a tower falls through 40m during last 2 seconds of it fall. The height of the tower is

Answer 1

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Answer 2

A body released from the top of a tower falls through 40m during last 2 seconds of its journey. What is the height of the tower?

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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 = 1/2 g (t-2)^2

And H = 1/2 g t^2

H also = 40 + d

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

Expand: 40 +5 (t^2 - 4 t + 4) = 5 t^2

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

Add like terms: - 20 t = - 60

t = 3 s

(t-2) = 1 second

In one second an object falls 5 m

Then H = 45 m

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Well body is released from the top of a tower means u=0

Let assume the hight of the tower is H

U' is the initial velocity of the body during last 2 second of it's journey

By using

S= ut + (1/2)g. t.t

Body falls through 40m during the last 2 second S= 40m,u=U' ,g= 9.81m/s^2

40=( U' 2 )+ ((1/2)*9.81*4)

Taking 2 common

20= U'+9.81

U'=10.19

Now using

V²=u² +2as

Here s = h

V= U'=10.19,u=0

a=g=9.81

10.19²= 0+2*9.81*h

h=5.2923598

Now the total hight of the tower is

H=40+5.2923598

The hight of the tower is

45.2923598

Q: A body released from the top of a tower falls through 40m during the last 2 seconds of its journey. What is the height of the tower?

A: 45.3 meters

Traveling 40 m over 2 seconds during constant acceleration of 9.8 ms^-2 and assuming no complications due to friction/wind/resistance etc would mean the average velocity during that period of 2 seconds was 40/2= 20 ms^-1

This would also be the instantaneous velocity 1 second before impact, allowing for 1 more second of acceleration.

The final velocity should be 20+9.8 = 29.8 ms^-1

The average velocity for the duration of the drop = 29.8/2 = 14.9 ms^-1

The time taken for the velocity to climb that high = 29.8/9.8 = 3.04 seconds

Total distance traveled = height of tower = 3.04*14.9 = 45.3 meters

If you did this problem using a=10 ms^-2 for nice round numbers, the answer would be 45 meters