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A stone is dropped from the edge of a roof, and hits the ground with velocity of -190 feet per second: How high (in feet) is the roof?...

Question

A stone is dropped from the edge of a roof, and hits the ground with velocity of -190 feet per second: How high (in feet) is the roof?

A stone is dropped from the edge of a roof, and hits the ground with velocity of -190 feet per second: How high (in feet) is the roof?



Answers

A stone is thrown vertically downward from the roof of a building. It passes a window $16.0 \mathrm{m}$ below the roof with a speed of $25.0 \mathrm{m} / \mathrm{s} .$ It lands on the ground $3.00 \mathrm{s}$ after it was thrown. What was (a) the initial velocity of the stone and (b) how tall is the building?

We know that a of CI is negative 32 feet per second squared. Therefore, what we know we can do is we can write this zero equals negative 32 time zero plus c. Thus, we know that seem must be equivalent to zero. Now, remember, they said the it hits the ground with the speed of 120 feet per second. And the problem therefore we know negative 32 teeth set equal to negative. 20. Remember the reason why it's night ofhis? Because actually moving downwards, we end up put three and 3/4 or 3.75 seconds. Therefore we know we can, right? A safety is negative. 32 terms 1/2 which is negative. 16 t squared plus eve to what she means. We can set this equal to zero giving us see if to solve equals 225 giving our final equation acid two's negative. So as of zeros, negative 32 were playing in zero plus R C of two we figured out was 225. This gives us 225 feet and this is our solution for the problem

First of all, we never acceleration. It's legal to know the sortie chew feet per second squared. So if we find V of tea, which is and how derivative of a 30 year view testicles no story to t plus C But we know obvious Darryl is equal to zero because they're starting velocity is zero. So if we said Stericycle to neighbor 30 to 10 0 plus see, we get seasonal to zero so therefore every of cheese but you may live 32 teeth. Next, we know that I hit the ground at a speed of ah, 120 feet person out of lost a 100 point feet per second. So we get negative 120 because this is the lost me is going downwards and is able to negatory to t So we get T is equal to three point folks 3.75 seconds. So you know that this is a time when it hits the ground. So next we know that the anti derivative of our Viotti is SSE which gets us night of 16 t squared plus d. And so first of all, we know that hits the ground at the time through front 75 seconds and we can choose to make ground level zero. So we have. Sarah is equal to negative succeed for 3.75 squared plus day. So we get d is equal to 225. And because when as a tea, when the time is zero. And this is when no time passed pass. And so this is one are this is why are stone is at the top of the cliff And so based off of this, we know that the stone was dropped from a height of 225 feet. So therefore the heart of the cliff must be equal to 20 Children. 25. That is our answer.

Right Iraq has thrown horizontally from a building with initial speed. Vienna equals 10.1 m per second. If it lands a distance D equals 57.1 metres horizontally from the base of the building, what is the height H of the building? This question is testing our understanding of the equations of projectile motion and the kinetics defined their end. So to answer this question, we need to define what is given in the problem and then use the equations to solve were given initial horizontal velocity 10.1. Initial vertical velocity zero. Because it's going horizontally extra equal zero. Why equals zero and X equals 57.1. Where we want to solve for why not? So we solve for T. Or the time it takes to the ground, X equals V. X nought T. So we solve for T. To get T equals X. B. X equals 5.65 seconds. Next we can solve for why not using Y equals why not? Plus B. Why not t minus half GT squared we have. Why not equals half Gt squared or 15.7 m? This is because V why not? T is zero as is why? And so we can simply solve for why not in this equation?

So here for party, we're gonna choose downwards to be positive. It's just much easier. Um, because if we don't have an initial, if you don't have an initial velocity going upwards against gravity, it's much easier just to, ah, consider downwards to be positive. So if we're moving with gravity initially, we can just add on essentially gravity. So ah, here we can use the equation to 15 and we can say Delta Y is equal ng b y initial t plus 1/2 Aah GT squared. We're gonna say Delta Y is 30 meters. Aah! This would be equal to our initial velocity. We have an initial velocity essentially of 12 meters per second so we can say 12 meters per second times t and then plus 4.9 meters per second squared times t squared. And if you wanted to solve, even, say, 4.9 t squared plus 12 t and then minus 30 meters, rather recon just minus 30. This would equal zero. And as you can see, this is a quadratic equation. So essentially Ah, you can use the salt function in your tea. I 84 85 89 in order to solve for tea, you're gonna get a negative answer and a positive answer. Of course, time can never be negative. So Time T would be equal to 1.54 seconds. This is the time needed to each the ground and for part B, we can save the wide final equals V. Why initial plus g t. So we can simply solve the wife final would be equal to 12 meters per second plus 9.8 meters per second squared multiplied by the answer. We had just found in part A 1.54 seconds and we solved that the speed wreck before it hits the ground is going to be equal to 27.1 meters per second. This would be our final answer for part B. That is the end of the solution. Thank you for


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