# Kinematic: Problem based on free fall

• NoahCygnus
In summary, a body drops from the top of a tower and covers a distance '7x' in the last second of its journey. It takes 'x' seconds to reach the ground.
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 .

NoahCygnus said:
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
cnh1995 said:
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## ?

NoahCygnus said:
it should come to a stop , doesn't that mean the final velocity should be 0?
No.
cnh1995 said:
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.

cnh1995 said:
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.

NoahCygnus said:
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?

cnh1995 said:
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##

NoahCygnus said:
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
cnh1995 said:
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 ?

NoahCygnus said:
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).

cnh1995 said:
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 ?

NoahCygnus said:
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.

NoahCygnus

## 1. What is free fall?

Free fall is a type of motion in which an object falls under the sole influence of gravity. This means that there is no air resistance or other forces acting on the object.

## 2. What is the formula for calculating free fall?

The formula for calculating free fall is: distance (d) = 1/2 x acceleration (a) x time (t)^2. This is known as the kinematic equation for free fall.

## 3. How does mass affect free fall?

Mass does not affect the rate of free fall. All objects, regardless of their mass, will accelerate towards the ground at the same rate due to gravity.

## 4. What is terminal velocity?

Terminal velocity is the maximum velocity an object reaches when falling through a fluid, such as air or water. It occurs when the force of gravity is balanced by the force of air resistance.

## 5. How can I use kinematics to solve free fall problems?

To solve free fall problems using kinematics, you must first identify the known variables (such as time, distance, and acceleration) and rearrange the kinematic equation to solve for the unknown variable. It is also important to pay attention to units and use the appropriate kinematic equation for the given scenario.

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