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.