Kinematic: Problem based on free fall

[NoahCygnus]

Homework Statement

"A body dropped from the top of a tower covers a distance '7x' in the last second of its journey where 'x' is the distance covered in the first second. How much time does it take to reach the ground ?"

Homework Equations

$S = ut - \frac{1}{2}gt^2$

The Attempt at a Solution

Displacement in the first second;
$-x = 0 - \frac{1}{2}gt^2$
$x = 4.9 m$
Displacement during last second;
$7x \longrightarrow 7(4.9) \approx 35 m$

That's all I could do. I don't know the distance covered between first second and last second , so I don't know how to utilise the current information I've to find the time .

 

[cnh1995]

I don't know the distance covered between first second and last second ,

What is the velocity of the body at the start of this interval? What is the velocity of the body at the end of this interval?

 

[NoahCygnus]

What is the velocity of the body at the start of this interval? What is the velocity of the body at the end of this interval?

Initially , it is 0 as the body is dropped from rest.
In the last second , I've no idea what the initial velocity is. Considering that the body hits the ground in the last second , it should come to a stop , doesn't that mean the final velocity should be 0? I'm not sure about it. If that's the case should i be able to find the initial velocity of the last second using the equation $v^2 - u^2 = 2as$ ?

 

[cnh1995]

it should come to a stop , doesn't that mean the final velocity should be 0?

No.

What is the velocity of the body at the start of this interval? What is the velocity of the body at the end of this interval?

In other words, what is the velocity of the body at t=1s? What is the velocity of the body 1 second "before" it hits the ground?

You need to use relevant kinematic equations involving time.

 

[NoahCygnus]

No.

In other words, what is the velocity of the body at t=1s? What is the velocity of the body 1 second "before" it hits the ground?

You need to use relevant kinematic equations involving time.

At t= 1,
$v = u - gt$ as u = 0 , t = 1 , it should be ;
$v= 9.8 m/s$

1 second before it hits the ground , I don't know how to get that. Help me out Sheldon.

 

[cnh1995]

1 second before it hits the ground , I don't know how to get that.

You know the displacement and time in this interval. Which equation contains these two terms with unknown initial velocity?

 

[NoahCygnus]

You know the displacement and time in this interval. Which equation contains these two terms with unknown initial velocity?

So the time interval is 1 second, using the equation
$-35 = u(1) - 5(1)$
$u = -30 m/s$

 

[cnh1995]

So the time interval is 1 second, using the equation
$-35 = u(1) - 5(1)$
$u = -30 m/s$

Yes. 30m/s downwards.

Now you have initial and final velocities in that interval. You can calculate the time from that.

 

[NoahCygnus]

Yes. 30m/s downwards.

Now you have initial and final velocities in that interval. You can calculate the time from that.

Final velocity should be
$v = -30 - 9.8$
$v \approx -40$
Now to find the total time.
$-40 = 0 -9.8t$
$t = 4 secs$
Right ?

 

[cnh1995]

Final velocity should be
$v = -30 - 9.8$
$v \approx -40$
Now to find the total time.
$-40 = 0 -9.8t$
$t = 4 secs$
Right ?

Right.
(Be consistent with the value of g. Use either 9.8m/s² or 10m/s²).

 

[NoahCygnus]

Right.
(Be consistent with the value of g. Use either 9.8m/s² or 10m/s²).

Thank you . And you said the final velocity won't be 0. I don't get it , does the body hit the ground at the last second. if so shouldn't the body come to a stop and final velocity be 0? Or you don't take into account the contact force ground will exert and don't even consider its there ?

 

[cnh1995]

Or you don't take into account the contact force ground will exert and don't even consider its there ?

The body hits the ground with some non-zero velocity.
Its velocity may become zero "after" it hits the ground (or it might bounce off) and that gets you into elastic-inelastic collisions. But whatever happens "after" the collision is a different issue. You only need to consider the time between the instant at which the ball is dropped and the instant at which it hits the ground. Only this interval describes the free fall of the body.