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In a mining site, bucket ore elevators are used to receive oresdropped from a certain point. One particular bucket moves up at 3.0m/s at an instant a lump of ore dr...

Question

In a mining site, bucket ore elevators are used to receive oresdropped from a certain point. One particular bucket moves up at 3.0m/s at an instant a lump of ore drops from a point 90.0 metersabove the ground, the bucket is 2.4 m above the ground. How farabove the ground will the bucket be when it catches the ore?

In a mining site, bucket ore elevators are used to receive ores dropped from a certain point. One particular bucket moves up at 3.0 m/s at an instant a lump of ore drops from a point 90.0 meters above the ground, the bucket is 2.4 m above the ground. How far above the ground will the bucket be when it catches the ore?



Answers

A rock is dropped (from rest) from the top of a 60 -m-tall building. How far above the ground is the rock $1.2 \mathrm{~s}$ before it reaches the ground?

So for this object that's thrown upward of eight meters per second, it wants us to find out how tall this cliff is by the time it reaches the bottom if it takes 2.35 So we list all of our knowns, including the fact that at the bottom of the cliff this position is zero and we used the equation. Position equals initial position, plus initial velocity times time plus 1/2 acceleration times, Times Square to our quadratic equation here. So when we plug in all of the numbers and look for the initial position, we find that it's 8.26 meters. So that's how told the cliff is compared to the bottom of the cliff, which is at zero. The next part of the problem asked us the stall for time, and this is a little bit trickier because it's asking us for time. If the rocks were thrown straight down at eight meters per second instead of up in the air. That means you don't actually know what its final velocity is when it hits the ground, which is gonna make our lives kind of dip cool. The reason why is because when we take all this information, the only equation we can use to directly solve for time is the same equation we use before. The sticking point is that we're looking for tea here, which means that T shows up in two different places in our equation. It shows up in initial velocity times time, and it shows up in 1/2 times acceleration times, Times Square because it's in both of these places at the same time. In order to solve for this, we have to use the quadratic formula, this all of it. Um, now a computer or a lot of calculators actually have a program in them that will solve this for you. So remember, when you're using the quadratic formula, whatever number is times X squared or in this case, T square, that's R a value. So you simplify 1/2 of negative 9.82 negative, 4.9, that's you're a value negative. Eight is gonna be our be value, because that's times t. And then the 8.2 sixes are CW. Now, the quadratic formula is always gonna give you two answers. But if you look at the two answers that it gives you one of them is negative, which doesn't actually make any sense for what we were solving because we were solving for time. So that means, um, the only answer that makes any sense based on the quadratic equation is that time is equal to 0.717 seconds. Now, if you're unable to do the quadratic formula, you could break this down into a two step problem instead to take all the same information. And instead of solving for time directly, you solve for final velocity at the bottom of the cliff first, and then you use that final velocity to pencil for time. So there's more than one way to solve this problem, but the most direct route is by using the my dreaded foot.

Question number 72. The initial velocity is your equal toe. It means that for a second let us take the downward direction as positive. So initially, this willow stays minus eight meter per second. That time is equal toe. 2.35 seconds. Are they the net? Downward displacement off the object is only the height off that lift. So using the second equation of motion, we can write the net downward. Displacement H is equal to my nest air, initially large in two time 2.35 is that gains last, uh, into x elation due to gravity 9.81 in tow 2.35 it's square. Solving this we will get the height off the cliff or the net Downward displacement Quito it point. Do it. Meet us. If the object is thrown downwards with the same villa speed, then you equally less it meters per second again using the second vacation off motion and let that time be E. We can write the height off the lift it want to. It is a quiet room. Initial velocity eight in two time d less, uh, indoor 9.81 He's where This is 1/4 ticket question and we will. When we will solve this, we will get the time equal to zero point 718 seconds.

This question asked us to find out How high would the Rocco. What we know is that we're looking at the driven it d of ass over D of teeth. We know we have 24 minus 9.8 t. We simply took the derivative. Now we know that if this is some equal to zero than solving, we end up with T 9.8 times T is equivalent to 24 which means to is T is 2.45 therefore US of 2.45 Plug back into this and we end up with 29.39 meters.

Let me draw figure Theis perpendicular equals l minus h and along the axe exes. We have maximum acts. This is the maximum accent deposit of X direction. And then hi, Part news equals l, right. And we know date t one, which is the initial kinetic energy equals heart em we square This is the initial kinetic energy. And to do, which is the kinetic energy 8.2 equals half m We two square seems to be two equals zero Therefore, Connecticut, an intricate 00.2 equals zero. And now from the figure we see date l minus each hold square, which is perpendicular plus base will base its x maximum. Ah, square equals elsewhere. Right. And this can be, uh, simply fine. And then we get it squared. Minus two l times, each less x squared. Maximum equals zero. No, let's solve for X maximum on then X maximum or maximum. X equals route. Ich into to l minus it. Right. So this is a cheer inch. Okay. And now again worked. And from 0.1 to 2 equals r t two minus t one. Well, this crumb equals minus m g etch. And then we have zero minus one divided by two m. These were right and solving for age EJ equals one divided by two multiplied by the square, divided by G where jeez acts relation due to gravity and each equals one divided by do multiply by, ah 10 square divided by G with these 32.2 and therefore height H equals 1.55 Do it beat right and then we have X maximum is equal to the Route 1.1 point 55 to eat into 60 minus 1.55 to it and therefore x maximum equals x maximum equals 9.539 point 53 feet.


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