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Arock is thrown upward from a bridge that is 29 feet above a road. The rock reaches its maximum height above the road 0.98 seconds after it is thrown and contacts t...

Question

Arock is thrown upward from a bridge that is 29 feet above a road. The rock reaches its maximum height above the road 0.98 seconds after it is thrown and contacts the road 2.26 seconds after it was thrown: Define a quadratic function;, f, that gives the height of the rock above the road (in feet) in terms of the number of seconds elapsed since the rock was thrown;{-8.359t*2-37.7841+29Preview

Arock is thrown upward from a bridge that is 29 feet above a road. The rock reaches its maximum height above the road 0.98 seconds after it is thrown and contacts the road 2.26 seconds after it was thrown: Define a quadratic function;, f, that gives the height of the rock above the road (in feet) in terms of the number of seconds elapsed since the rock was thrown; {-8.359t*2-37.7841+29 Preview



Answers

A stone is thrown directly upward from a height of 30 ft with an initial velocity of $60 \mathrm{ft} / \mathrm{sec} .$ The height of the stone, in feet, $t$ seconds after it has been thrown is given by the function $s(t)=-16 t^{2}+60 t+30 .$ Determine the time at which the stone reaches its maximum height and find the maximum height.

In this problem, we are given a function and it represents a person standing on a cliff that is 100 ft hi And then throws a rock off the cliff. So my curve represents the path of the rock and it throws up in the air and then the rock goes back to the ground. The X axis represents time in seconds. So after how many seconds does it take for the rock to reach the maximum height? So that's going to be our vertex which is right here at one second, it is going to reach a maximum height of 116 feet. Okay. And then the next thing we can tell is how long does it take the rock to travel up in the air and then return or hit the water? So That's going to be represented by this x intercept here. It takes approximately 3.7 seconds for the rock to hit the water. So the first one, the maximum height is represented by our vertex. And the second one, when it hits the water is represented by one of our X intercepts. There is a second X intercept, but it does not play into this problem situation. So you want to make sure that when you're solving for your X intercepts, you choose the one that makes sense for the problem given, and in this case It is gonna be the positive x intercept at approximately 3.7.

We are given The function gives the height s that says minus 16 t squared plus study duty plus 1920. We are given for the first question that we need to find the times at which hide exceeds 1920. So that is going to be a softy greater than 1920. That's gives us minus 16 piece. We're blessed. We do the last 1920 craters on 1920 That's gonna be minus 16 piece where plus heavy duty created an zero. This is going to give us the value off key, as you know on Do then me find solution said by looking at it doubles A B and C start by taking a value. And then there will be that's going to be between zero and two. Let's take as one for this while you get s off T. That is greater done. 1920 Clearly so this and double excluding zero and do its part off solution said Then we can expect that day and see will probably don't be so for being hated. And so that's the equal. Three. We get a softy less than 1920. You don't need to calculate this event by inspection, you can figure out that it's less than 1920 on for endurable be. That was for a value less than zero ut minus one we didn't get that s softy. Turns out to be less than 1920. Hence, the solution said, does open dragons Ito, Come on, then. In the second question, that is, Barbie it us that for what times is the height? Less than 6 40 So it s off t less than 6 40 black. And on we get minus 16 days. Where blessedly duty. Yes, Well, 80 less than zero. We find the root off this equation by putting the values of ABC for this quadratic equation. Inside are quadratic formula. You can take your time with this. That is absolutely fine. Once this is stumping, get the values t minus eight on we set up the end. Erwin's figured out that 40 less than minus eight on for that s softy is less than 6 40 for the less Stanton greater than minus eight hours. Off these craters on 6 40 p. Leader. London s obvious leads at 40. Solution said as minus infinity call minus eight. Union 10 coma. Infinity

We are given The function gives the height s that says minus 16 t squared plus study duty plus 1920. We are given for the first question that we need to find the times at which hide exceeds 1920. So that is going to be a softy greater than 1920. That's gives us minus 16 piece. We're blessed. We do the last 1920 craters on 1920 That's gonna be minus 16 piece where plus heavy duty created an zero. This is going to give us the value off key, as you know on Do then me find solution said by looking at it doubles A B and C start by taking a value. And then there will be that's going to be between zero and two. Let's take as one for this while you get s off T. That is greater done. 1920 Clearly so this and double excluding zero and do its part off solution said Then we can expect that day and see will probably don't be so for being hated. And so that's the equal. Three. We get a softy less than 1920. You don't need to calculate this event by inspection, you can figure out that it's less than 1920 on for endurable be. That was for a value less than zero ut minus one we didn't get that s softy. Turns out to be less than 1920. Hence, the solution said, does open dragons Ito, Come on, then. In the second question, that is, Barbie it us that for what times is the height? Less than 6 40 So it s off t less than 6 40 black. And on we get minus 16 days. Where blessedly duty. Yes, Well, 80 less than zero. We find the root off this equation by putting the values of ABC for this quadratic equation. Inside are quadratic formula. You can take your time with this. That is absolutely fine. Once this is stumping, get the values t minus eight on we set up the end. Erwin's figured out that 40 less than minus eight on for that s softy is less than 6 40 for the less Stanton greater than minus eight hours. Off these craters on 6 40 p. Leader. London s obvious leads at 40. Solution said as minus infinity call minus eight. Union 10 coma. Infinity

Approaching 47 in order to grab the velocity since the velocity function is a line and we must be not negative So we can use the intercept to the graft function. So at is equal to zero me off zero is equal to 48 32 times zero is 48 eso The one point is zero and 48 So access equal to zero. And why is ableto 48? This is the first point and the second point when we off t is equal to zero So 48 minus 32 he is equal to the authority is equal to 1.5 for the second point is that it's t is equal to 1.5 and we lost is equal to the roof. Is this point with this point is ah is 0.0 and 48 and this point is 1.5 and ends here and this is the function off the deal for question be eso using this using this breath. The rock is through a straight off the next month while it reached for in being off these April 20 which is is able to 1.5 So this is the maximum fine for questions. Scene. The distant troubled by the rocks is the same as the area under and under that under the grass off the velocity function over the interval from 0 to 1.5. So using that graph from the force of the area is, uh, into the area off the trend is half pace, which is 1.5 times five fifties 48. So is equal to 36 spirit. This is the distance troubled by the rock.


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