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## Class 9 Physics (India)

### Course: Class 9 Physics (India) > Unit 3

Lesson 3: Motion of objects in the influence of gravitational force of earth# Free fall 1 body - solved example

Let's solve problems on one body in free fall. Created by Mahesh Shenoy.

## Want to join the conversation?

- At8:55I think we can use the equation which has time. We know that a=v-u/t, we know v and u and a, so we can calculate t and use the equation with t in it.(5 votes)
- You can do it like that, but it would be a time waste if we first solve for time and then use the equation while we have another for which we do not need time.(1 vote)

- At2:00he says that when an object speeds up it means the acceleration is positive but when its speed is decreasing, the acceleration is negative, but in the practice they consider upward movement as positive and downward as negative and I'm not able to understand it. Can someone please explain this?(4 votes)
- When u jump them there comes a time when u reach a maximum height and then start falling down. Why does this happen? This is because of acceleration due to gravity. Why do u slow down when u jump? Its because of g. So when u jump u go against g therefore it is negative. Similarly when u fall u seem to speed up some how, this is where u go with g therefore it is positive

Going up= going against acceleration due gravity = negative g

Falling = going with acceleration due to gravity = positive g

( g here means acceleration due to gravity)(2 votes)

- When to take “g” negative?(1 vote)
- Whenever the direction of motion (taken positive) is against gravity(i.e. upwards), g is taken as negative. Negative value actually means nothing but something in an opposite direction
*Hope that helped. Feel free to comment if you doubt persists :)*(5 votes)

- What is a definition of Free Fall?(2 votes)
- Free fall means when there is only one force acting on the body which is the gravitational force.(2 votes)

- Physics is hard enough without switching up the variable letters. I f this is an AP physics lesson, then please use the symbols that the course uses.(1 vote)
- @2:00he considered the acceleration is negative, but in previous videos they take the acceleration is negative and displacement is negative in downward direction as in projectile motion videos , Could anyone explain what is the difference?(1 vote)
- maintain consistency in your videos and the practice questions. in the video, he says whenever something goes up, its acceleration due to gravity is
**negative**because 'it slows down'. in the practice questions, however, the upward movement is**positive**. this has confused me to no ends as to what to consider between the two conventions.

i made so many mistakes in the practice numericals' positive and negative signs just due to this confusion.(1 vote) - In the spiderman example the initial velocity should also be zero since the object is jumping which means it is moving upwards from rest to motion. Pls clear my doubt.(1 vote)
- Intial velocity wouldn't be 0 because he jumps with a velocity of 20m/s. That means he uses that 20m/s to escape the force of gravity to attain a certain hieght.(1 vote)

- At2:02he says that negative acceleration and deceleration are the same and when an object has a positive acceleration, it is speeding up. Is this true? If an object is moving towards the left (in a coordinate plane where right is positive) and is speeding up, then his acceleration would be negative, but it wouldn’t be decelerating.(1 vote)
- In case of gravity if the object is speeding up the acceleration has to be positive since the the speed is increasing. And it the object is slowing down as in the spiderman case then the acceleration will be negative. Nowhere did the instructor talk about the coordinate plane here.(1 vote)

## Video transcript

- [Instructor] Let's
solve a couple of problems on falling things. Here's the first one, Deadpool drops from a height of 45 meters. Find the time it takes for
him to reach the ground. G is 10 meters per second squared. So let's look at what's given to us. We have Deadpool, who's dropping
from a height of 45 meters. So let's draw a diagram. Here's our Deadpool, a superhero who always puts his maximum
efforts in catching bad guys. He's dropping from a height of 45 meters. That means the height right now
is this height is 45 meters. We need to find the time it takes for him to reach the ground. So how do we solve this? Well, remember that
whenever things are falling under gravity, they have
a constant acceleration of 9.8 meters per second squared. In this problem, they've asked
us to round it off to 10. So this is the acceleration
with which Deadpool is gonna fall. Okay, so what? Well, whenever something
has a constant acceleration then we can use three equations
of motion to solve them, where V is the final velocity. U is the initial velocity,
acceleration, time and S is displacement. Now, if you're not familiar
with this equation, so you need a refresher, great idea to go back and
watch videos on equations of motion, and then come back over here. And so we'll write down what's given to us and what is asked and we'll
see which equation to use to solve the problem. Okay, it's given the Deadpool drops from a height of 45 meter, which means he's gonna fall down. He's gonna displace by 45 meters. So we know the displacement is 45 meters. We also know his acceleration, his acceleration is going to be 10 meters per second squared. Now what's important is
accelerations can be both positive and negative, wherever objects speed up, this means the acceleration is positive. And whenever objects slow down, we say that exploration is negative. So in this example, notice
Deadpool is gonna speed up as he falls, he's gonna go
faster and faster, right? And so in our example, we'll take acceleration to be positive. What else has given? It seems like it's only these
two things are given, right? But there's on one more information, which is pretty important. It's given the Deadpool drops
from the height of 45 meters. Whenever something is dropped, we know it's initial
velocity is zero, okay.? So we know the initial
velocity of Deadpool, that is zero and we are calculate
the time it takes for him to reach the ground that means
we need to find what T is. So now we just have to
select which of the equation we can use to solve the problem. And before I do that over
here, great idea to pause video and see if you can choose, you can select which
equation you would use to solve this problem. All right, let's go through
each question one by one. Can we use the first one? No, because the first one has
V in it, which we don't know. Can we use the second one? We know S we know U and we know, A. Hey, we can use the second equation. We can go for this equation. What about the third one? The third one doesn't even have T in it. So even third one we can't use. So we have a winner and we're going to use
equation number two, and substitute and solve the problem. And again, if you didn't solve it earlier, now would be a great time to, again, pause and see if you can
go ahead and plug in. Okay, let's go ahead and substitute. S is 45 meters that
equals U, which is zero. And so this whole term goes to
zero, which I will not write. Plus half times A which is
10 meters per second squared, times T squared. And now all we have to
do is solve this equation and we'll be done. So let's simplify this. Let's see what we get. Two goes five times and our
meter cancels over here. And the five goes nine times over here. So what do we have? We have nine on the left-hand side and we have T square
on the right hand side divided by second squared. So if I multiply by second
square on both sides, I will now get nine... Let me know that over here, I get nine second
squared equals T squared. And now, since I want
to calculate what T is, let's take the square root on both sides. Squared of nine is three, squared of second square
is seconds equals T. And there's an answer,
so T is three seconds. That means Deadpool takes
three seconds to land on the ground. Now, before we proceed, one question we might have
is squared of nine is both Plus three N minus three, right? So why did we ignore the minus three? Well, because if time is minus
three, it is less than zero. And that represents the
past because time is zero is the present it's right now. So, less than zero that present past, more than zero represents future. Since we are asked to calculate
how long it takes for him to reach the ground after he has dropped, we care about the future. And it's for that reason, we only consider the positive time. And so you'll see most
of the physics problems, whenever we're asked to calculate the time since we were asked about the future, we only consider the positive ones and we'll ignore the negative
ones, so negative values. So anyways, let's now
consider another problem. Spider-Man jumps straight up with the speed of 20 meters per second, calculate the maximum height he reaches. Again, given G is 10
meters per second square. Can you try to solve this one yourself? Again, make a quick drawing of this. See what is given what is asked and then pick an equation to use. All right, let's see. So we are given that the
Spider-Man is jumping straight up, so let's draw that. So here's our Spider-Man, who's jumping straight up with the speed of 20 meters per second, we need to calculate the
maximum height he reaches. So eventually he would
reach a maximum height and then start falling back, right? So we need to calculate
what that maximum height is. What is that distance? So again, let's write
down what's given to us. We know that initial velocity
with which Spider-Man jumps. So we know U that is 20 meters per second. We also know the acceleration. Whenever things are falling under gravity, immediately we know it's acceleration. Acceleration is going to be now this time, is it going to be plus or minus 10? Well, this time where
as Spider-Man goes up, he slows down, right? He slows down as it is
that he's losing velocity. And since he's losing velocity, the acceleration becomes negative. It's a deceleration right? So the acceleration
becomes minus 10 meters per second squared. Again, that's the
important part over here. What else is given? Again it feels like these are the only two
things given, right? But something else is also given. Again, this is super
important to figure out. We are asked to calculate
the maximum height. And at the maximum height, we know the velocity of Spider-Man. At this point, if this
is the maximum height, his velocity must be zero. That means we know his
final velocity is zero. How do we know that? Why is it so? Well think about it, if Spider-Man did not have zero velocity, if say he was still going
up with some velocity, then this wouldn't be the maximum height he's yet to reach the
maximum height, isn't it? On the other hand of
Spider-Man was going down with some velocity, tat
means he has already reached some maximum height, and
now he's coming downwards. So the only possible
velocity for Spider-Man at the maximum height must be zero, right? Think about this. All right, and what we are asked. Well, we are asked to
calculate that maximum height. So in this case, we're asked
to calculate the displacement. That's what we need to know
the displacement of Spider-Man. Again, which equation do we go for? Now, again, if you want
to try this on your own, great idea to pause and see
which equation you would go for, but let's see, we can't
use the first equation because it does not have S, it is useless. What the second equation, hey, we can't use that
because there's a T in it. And we don't know the time. So that only leaves us
with the third equation. And so we can use equation number three. And if we substitute these values, which I'm pretty sure you can do now, we will get zero equals 20
meters per second squared, plus two times minus 10 meters
per second square at times S and to save time, I'm pretty
sure you can do this yourself. I'll tell you what the final
answer turns out to be. If you calculate that, if you simplify, you will get the displacement
as to be 20 meters. That means Spider-Man reaches
a maximum height of 20 meters. And so whenever things
are falling under gravity, because they have a constant acceleration, we can always use the
three equations of motion and solve our problems. Now, there are a couple of things to be careful about though. One is the sign of the acceleration. When objects are thrown up, because their velocity will decrease, our acceleration will be negative. If the obliques are thrown down, the acceleration becomes positive. Another thing is sometimes the
data is not given directly. It's a little hidden. For example, if we were given
it reaches maximum height, but we had to understand
that maximum height means the final velocity is zero. Similarly, in the previous problem, it was given that he drops from a height. We had to understand that drops means that initial velocity is zero.