A volcanic block is ejected at an angle of 45 degrees from Mount Fuji during a volcanic eruption. It lands at the foot of the volcano at an horizontal distance of 9.4 km. The height of Mount Fuji is 3.3 km. What is the block's initial speed? Do I use Pythagorean theorem to find the hypotenuse? Is my distance known?

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A volcanic block is ejected at an angle of 45 degrees from Mount Fuji during a volcanic eruption. It lands at the foot of the volcano at an horizontal distance of 9.4 km. The height of Mount Fuji is 3.3 km. What is the block's initial speed? Do I use Pythagorean theorem to find the hypotenuse? Is my distance known?

Physics
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I got the formula x=x(initial)=v(inital x)*t+1/2at^2
Nope you would use this formula \[R=\frac{ v _{i}^2\sin2\theta }{ g }\] where R is the horizontal distance it traveled vi is intial velocity theta is the angle g is the acceleration of gravity
Your formula is incorrect because it is a 2 dimensional motion (x and y component changes) You can ignore the height of the volcano

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But to find R convert the horizontal distance of km to meters
The think is I never learned that formula/ This is a calc base physic. So I need to to get the velocity by figuring out what I have. I drew a triangle with the angle I get \[V _{0x}= v _{0}*\cos(45)\] \[V _{0y}= v _{0}*\sin(45)\]
besides I don't know what's R and the initial velocity
You would need initial velocity to use that formula of yours. It would be the x and y component of the initial velocity. Where were you given "that" in the question?
there is not a initial velocity. This is suppose to make you find it. So I was thinking. when t(time) is 1/2 does that equal 0 for the y component since it is tangible half way making no velocity when time reaches 1 half of it's destination?
\[v _{xi}=v _{i}\cos \theta \] \[v _{yi}=v _{i}\sin \theta \]
I did that. But what V initial?"
Thats what I said. You mentioned the formula I wrote and I told you that it wasnt needed.
But I dont think my professor wants to see that since I have not learned it yet. He want's me to use what I have which is the distance formula and velocity/
so the v( y initial) is irrelevant?
You sure? Check your notes or online lessons?
yes. for a thrown object, a=g v=gt+v x=1/2 t^2 + v(initial)
Its a projectile motion. |dw:1443681041543:dw| It is 2D dimensional
and for the y component, \[y _{0}+V _{_{0y}}+\frac{ 1}{ 2 } a _{y}t ^{2}\]
Yes I know. so I need to take account of gravity. SO if it takes x(time) to reach 9.4 km. In half time it reached half it's distance correct?
It doesnt work that way. The y component only works on 1d This is 2D |dw:1443681204247:dw|
I dont ge tit
Follow my instruction by using the formula I mentioned in the beginning and you will.
but the initial velocity is still unknown. I want to learn it by solving velocity with the projectile motion.
Look. \[h=y _{f}\] \[h=y _{i}+v _{yi}t-\frac{ 1 }{ 2 }g*t^2\] \[h=v _{i}\sin \theta \times \frac{ v _{i}\sin \theta }{ g }-\frac{ 1 }{ 2 }g*(\frac{ v _{i}\sin \theta }{ g })^2\]
\[t=\frac{ v _{i}\sin \theta }{ g }\] since \[v _{yf}=v _{yi}-g*t\] \[0=v _{i}\sin \theta-g*t\]
So \[h=\frac{ v _{i}^2\sin^2\theta }{ 2g }\]
isn't it g^2?
But that equation is useless. We dont know the height from the volcano to the highest point.
So instead we use this one I mentioned earlier.
it 3.3km
\[x _{f}=x _{i}+v _{x i}t \rightarrow R=v _{x i}t \rightarrow (v _{i}\cos \theta)2t\]
\[(v _{i}\cos \theta)\frac{ 2v _{i}\sin \theta }{ g }=\frac{ 2v _{i}^2\sin \theta \cos \theta }{ g }\]
\[R=\frac{ v _{i}^2\sin2\theta }{ g }\] R should be in meters, so convert it first.
x(initial) is zero since it is not given. There was some acceleration so all I am left with is v*a*t^2 +v(initial)*t
h is the max height it reaches at its starting point. We dont know that. |dw:1443682444669:dw|
45 angles thrown off from a cliff is the same distance as 45 angles thrown from the ground. So height of the volcano is irrelevant.
it erupt. there must be some speed for the vertical but how is there an innital for the horizontal component?
Its a projectile motion. It goes both ways.
All I can say is use my formula with the R. If you're not going to listen to me, why ask the question?
ok.. So how do i get velocity?
@Shalante what v then?
Look at my first posts.
thanks. It is still confusing. I just trying to make sense in my perspective
R has to be meters. The horizontal distance of 9.4 km is kilometers. Did you convert it?
What are you confused at?
the height of the volcano is certainly not irrelevant in this question you have correctly identified that, if the initial velocity of the rock is v, then it's horizontal and vertical components are both \(\dfrac{v}{\sqrt{2}}\) for total flight time t, in the horizontal direction you can say that \(\frac{v}{\sqrt{2}} t= 9400\) as velocity is assumed to be constant [no air resistance etc] in the vertical direction, using your equation \(x = v_{i}t + \frac{1}{2}at^2\) we can say that \(-3300 = \frac{v}{\sqrt{2}} t + \frac{1}{2} (-9.8) t^2\) [positive is up, ie note signs] that simplifies nicely: \(-3300 = 9400 + \frac{1}{2} (-9.8) t^2\)
iRISHBOY How did you get v/sqrt(2)? I got the solution but i don't get what my professor did
How do you solve this type of problem. I am taking quantitative physic
No. The x and y components are separated and they are 2 different equation \[y _{f}=y _{i}+v _{y i}t+\frac{ 1 }{ 2 }a _{y}t^2\] \[x _{f}=x _{i}+v _{x i}t+\frac{ 1 }{ 2 }a _{x} t^2\] Sure, I agree that \[(v _{x i}\cos45)t\] equals\[\frac{ v }{ \sqrt{2} }t=9400 \] but If the acceleration is gravity (9.8m/s^2) then this formula have to be in y component, including the height (yf): \[y _{f}=y _{i}+v _{yi}t+\frac{ 1 }{ 2 }a _{y}t^2\] and \[v _{x i}t=9400m\] \[v _{yi}t \neq v _{x i}t =9400m\]
\[x _{f}= v _{x i}t\] if velocity of horizontal component is constant. \[y _{f}=v _{y i}t\] The acceleration always changes in the y direction. (gravity) So \[x _{f}\neq y _{f}\]
@Venomblast \(\cos 45 = \sin 45 = \dfrac{1}{\sqrt{2}}\)
\[\tan(45)=\frac{ v _{y} }{ v _{x} } => 1=\frac{ v _{y} }{ v _{x} } \] Thus they're both equal. Ok what do I do now? I will upload my work
What do I do now?

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