Video Transcript
If a body, which was dropped from a building, took three seconds to reach the ground, find its average velocity as it fell. Let the acceleration due to gravity ๐ equal 9.8 meters per second squared.
Okay, so in this question, what we have is a body being dropped from a building. So, in the little sketch here, weโve got here our body being dropped from a building. What we can see is because itโs traveling downwards, as itโs come from the edge of a building, then this means that the positive direction weโre gonna consider is the direction towards the ground.
We also know that its acceleration due to gravity is 9.8 meters per second squared. And this is a constant acceleration. So therefore, we know thatโs a constant-acceleration problem. So, we can use our ๐ ๐ข๐ฃ๐๐ก equations. And the equations of constant acceleration are often known as the ๐ ๐ข๐ฃ๐๐ก equations because of our variables. We have ๐ which is our displacement, ๐ข our initial velocity, ๐ฃ our final velocity, ๐ our acceleration, and ๐ก our time.
Well, in this problem, we donโt know ๐ because thatโs our displacement cause we donโt know how far it is from the top of the building to the ground. Well, we know that ๐ข, our initial velocity, is zero. And thatโs cause the body is dropped from a building. So therefore, it was stationary at the beginning. We donโt know ๐ฃ, our final velocity. We know that the acceleration is 9.8 because itโs the acceleration due to gravity. And itโs gonna be positive 9.8 because weโve decided that the downward direction is our positive direction. And the ๐ก, our time, is equal to three. And thatโs because it took three seconds to reach the ground.
Okay, great. So now, whatโs the next step? Well, what we have are five different constant-acceleration equations. We actually have different versions of these as well. Sometimes, people rearrange them. But these are often the five that we use. So, weโve got ๐ฃ equals ๐ข plus ๐๐ก. ๐ฃ squared equals ๐ข squared plus two ๐๐ . ๐ equals ๐ข๐ก plus half ๐๐ก squared. ๐ equals ๐ฃ๐ก minus a half ๐๐ก squared. And ๐ equals a half multiplied by ๐ข plus ๐ฃ multiplied by ๐ก.
Well, first of all, what weโre gonna try to do is find ๐ , our displacement. And we know ๐ข, ๐, and ๐ก. So therefore, what weโre gonna do is weโre gonna use equation three, ๐ equals ๐ข๐ก plus a half ๐๐ก squared. So, what we get when we substitute in our values is ๐ , which is what weโre looking for, is equal to zero multiplied by three โ cause thatโs our ๐ข multiplied by our ๐ก โ plus and then weโve got a half multiplied by 9.8 multiplied by three squared. So what weโre gonna get for ๐ , our displacement, is zero plus 4.9 multiplied by nine, which is gonna be equal to 44.1 meters. So great, weโve now found our displacement.
Well, have we finished there? Have we solved the problem? Oh, no because what weโre looking for is the average velocity. But what we have is a formula to help us. And what that tells us is that the average velocity is equal to the total displacement over time, which is going to be equal to 44.1 over three. So, this is gonna give us a final answer of 14.7 meters per second. And this is going to be the average velocity of the body as it fell.
