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A certain freely falling object, released from rest, requires 1.50 s to travel the last 30.0 m before it hits the ground. (a) Find the velocity of the object when i...

Question

A certain freely falling object, released from rest, requires 1.50 s to travel the last 30.0 m before it hits the ground. (a) Find the velocity of the object when it is 30.0 m above the ground. (b) Find the total distance the object travels during the fall.

A certain freely falling object, released from rest, requires 1.50 s to travel the last 30.0 m before it hits the ground. (a) Find the velocity of the object when it is 30.0 m above the ground. (b) Find the total distance the object travels during the fall.



Answers

A certain freely falling object, released from rest, requires 1.50 s to travel the last 30.0 m before it hits the ground. (a) Find the velocity of the object when it is 30.0 m above the ground. (b) Find the total distance the object travels during the fall.

We assume the object starts from rest and first we consider the last 30 meters off before we'll find in speed 30 meters above the ground using the equation. Why, if is equal to why I so its final position is equal to is its initial position. Plus its initial velocity times, time t best 1/2 a t squid. So we know its final position. Zero we had reached the ground and its initial position is 13 meters plus its initial velocity for the last 30 meters. But you want to calculate and the time tee off 1.5 seconds plus, huh? And the acceleration is minus 9.8 meters per second squared, which is the gravitation acceleration, acting opposite to the displacement much better by the time t of 1.5 seconds square. And so if we calculate for the initial velocity V, I start off the last 30 meters, we get the I two B minus 12 or in six. Meat is a second. So no, we want to calculate what happens before the last 30 meters. So we considered a portion of the fall above the 30 me to point and we used the equation. The F squid is equal to the ice were thus to a into why f minus Why I So the F squared in this case is the I squared from the first part. The initial velocity for the last 30 meters is the first the final velocity when you've reached the point So again we can substitute values into this operation. So that's minus 12.6. It is a second. Well, squid is equal to its initial velocity. We assume starts arrest that zero bus to times gravitation exploration is minus 9.8. He just square second comes down to why we were used to calculate. And so again, if you re arranging solved without a why we get outta why is equal to minus eight 0.16 meet us so therefore we can calculate the original height wins the show. So the original height, at which point this object was addressed, is equal to 30 meters. Thus, 8.16 it says agains started journey of my height off 38 Going to each is above the code

So here's a bit easier to choose downwards to just be positive. And so we can say that, Um four. If we say this, we can say that. Why finalists? Equaling 75.0 meters and we can choose the the place with which the object has dropped? Why initial This would equal zero meters and so for part A. When we say that why final equals y initial plus V y initial T plus 1/2 GT squared well in the 1st 2nd Why initial is equaling zero ve y initial is equaling zero. So both of these are zero. And so why final would be equaling 1/2 times 9.8 meters per second. Squared times 1.0 seconds Quantity squared. This is simply equaling essentially 4.90 meters. So it's traveled 4.90 meters in the first in the 1st 2nd and then it's saying, um essentially, what's the speed with which it hits the ground? If again we're choosing downwards to be positive, we expect the positive velocity we should take note of this downwards is positive. And so we can say that V why final squared equals the my initial squared plus two times the acceleration due to gravity times Delta y. And in this case we know that initially we don't have any velocity in the wider action. So V why final is equaling the square root of two G delta y and we're traveling 75 meters. So this is equaling. The square root of two times 9.8 meters per second squared multiplied by 75.0 meters. Now we can say that V Y Final is gonna be equal and positive 338.3 meters per second. And all we have to do is just note. This is downwards, so it depends on the situation. But sometimes choosing downwards to be positive makes calculating everything much, much easier. And then we have to. For part C, we want to determine the distance traveled during the last second of motion before hitting the ground. So now we have a time where it's the last second. And so we can say that first, for part C, let's find a total time. So V why final equals V. Why initial plus g t now b y initial, we know zero so tee total with the equaling here 38.3 meters per second. Divided by 9.8 meters per second squared. This is equaling 3.91 seconds. So we wantto essentially find t the position at 3.91 seconds minus 1.0 seconds. This, of course, 2.91 seconds. And so we can say that here. No. How far did it travel in? How far did it travel in, um, 2.91 seconds. So we can say that first why final is equaling 1/2 times 9.80 meters per second squared multiplied. By here it would be again 2.91 seconds. Quantity squared 6.5 times 9.8 times 2.91 times 2.91 This is equaling 41.5 meters. Now we know that the total drop was 75 meters. So essentially we can then say that in the last second the object travels and this would be 75 meters minus 41.5 meters, cause in 2.91 seconds. That's how far I traveled. So in the last second, it must travel the rest of the distance. 75 minus 41.5. So in the last second, the object travels 33.5 meters. This would be our final answer for part C. That is the end of the solution. Thank you. For what?

So here. Ah, we're going to be using Equation 4 21 and for 22 and the initial angle is equaling negative 20 degrees, so we can then use the initial velocity equaling 15.0 meters per second. We can then say that Delta acts is going to be equal and blossom. The initial co sign the fate of initial multiplied by t and here we can say that this would be equaling 15.0 meters per second times co sign of negative 20 degrees multiplied by 2.30 seconds and this is giving us 32.4 meters. Four part. This would be for party for apart be than the vertical displacement would be equaling two velocity initial sign of data initial multiplied by T minus 1/2 GT squared. So this is giving us 15.0 meters per second sign of negative 20 degrees multiplied by 2.30 seconds, minus 1/2 multiplied by 9.8 meters per second squared multiplied by 2.30 seconds. Quantity squared and we find that delta Y here is equaling negative 37.7 meters. This would be our final answer for Part B and our final answer for party above. That is the end of the solution. Thank you for watching.

Yeah. This question because the concept of free fall and we are going to use this to patient to solve this problem since the ball is strong vertically report. Okay, so at the maximum hide the final speed. That is me. Why have will become 00m Massacre? And from the question when sir part Okay, we can try the time it takes to reach the maximum altitude. It's zero majors possible minus viv I I. And that is 15 m For a second. Upon the acceleration number vertical direction that has managed 9.8 m for 2nd square At the time to equals 1.53 seconds. No five seed. Yeah, the maximum to do ah, this can be found with the second equation uh h equals zero minus 15 leaders for second squared upon to into the graduation acceleration There is minus 9.8 m for second square at the maximum altitude. Excuse 11.5 weeks. Our part C the velocity along the right direction is the velocity, initial velocity that is 15 m or second minus, sir Value of G. That is 9.8 m for 2nd square into the time. And the time tears uh, two seconds. So the velocity at T equals two seconds is -4.6 m for 2nd. And since the motion is a freefall motion, therefore, the acceleration at that moment is -9.8 m for 2nd square, it will be constant for all time.


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