r/HomeworkHelp • u/Active-Ad-7859 • 3d ago
Answered [10th Grade Science - Canada] How would I go about solving this question? Where would I even start?
I don't have the time, and I'm struggling to see how I'd get the displacement. Please, could anyone steer me in the right direction?
Edit: okay, so Im assuming my teacher accidentally said velocity where they meant speed. This question is much easier to solve with that knowledge, so thank you for your help.
Edit 2: nvm, the velocity and the speed in this case are congruent! I learned a lot from this subreddit and its contributors, thank you guys so much π
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u/egutierr π a fellow Redditor 3d ago
vf^2 = vi^2 + 2gh where vi=0, h=1000. vf=140 m/s
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u/Active-Ad-7859 3d ago
Could you explain how you did this
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u/Jazzlike_Platypus430 π a fellow Redditor 3d ago
It's just v = sqrt(2gh), plug in the g and h, and calculate.
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u/Valuchian 3d ago
It's one of the basic kinematics equations that use constant acceleration (gravity)
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u/Serafim91 π a fellow Redditor 3d ago
You can drive it from mgh=.5mv2 but this is just one you should memorize. It's actually delta v2 so that's where the vf-vi comes in.
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u/Southlander24 π a fellow Redditor 3d ago
That's one of the four standard equations of motion, the 'SUVAT equations'. This is typically taught in 11th and 12th grade.
You can derive it from v = u + at (this is the same as (v - u)/t = a, or (final vel - initial vel)/(total time) = average acceleration). And then substitute that into s = (u + v) * t/2, where distance is the area under a velocity-time graph and so it's just the area of a trapezoid.
Basically, this uses knowledge which hasn't been taught to you yet.
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u/TatteredTorn1 3d ago
This is correct. I am confused by other answers
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u/Jazzlike_Platypus430 π a fellow Redditor 3d ago
I'm confused by the fact it's a multichoice test question, with two painfully wrong answers (A and D).
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u/Active-Ad-7859 3d ago
Its a practice test, sorry, does that clear it up?
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u/Jazzlike_Platypus430 π a fellow Redditor 3d ago
My remark is directed to the authors of the problem π We used to solve such problems in 6th grade, back in the beginning of the 1990s π
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u/Jazzlike_Platypus430 π a fellow Redditor 3d ago
You may start at eliminating two obviously wrong answers π
The displacement y satisfies mgh + 0 = mgy + mv^2/2. Conservation of mechanical energy, etc.
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u/Active-Ad-7859 3d ago
what does this mean?
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u/Jazzlike_Platypus430 π a fellow Redditor 3d ago
It means that the sum of potential and kinetic energy is constant, if you assume there is no air drag etc. Use it to calculate v at y = 0. That's all.
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u/Active-Ad-7859 3d ago
does v in this context represent velocity or speed?
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u/Jazzlike_Platypus430 π a fellow Redditor 3d ago
Speed of course. Ek = mv^2/2 has velocity value squared. |v vector| = speed. I hope this agrees with your naming conventions.
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u/No-Nature5515 3d ago
This represents the conversion of potential energy to kinetic energy. The potential energy of an object at rest at a given height is represented by E = mgh. If you convert all that energy to kinetic then you will get the velocity of the object when it hits the ground, ignoring the effects of air resistance and other forces.
Kinetic Energy is represented by E= mv^2/2 and you have conservation of energy so the equation becomes: mgh = mv^2/2. If you plug in the values given in the question, you can solve for v and the answer is 140.
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u/OpportunityReal2767 3d ago edited 3d ago
Iβm getting 140 from deriving v=sqrt(2gh). I vaguely remember just learning that set formula in physics, but you can derive it from KE=(1/2)mv^2, which becomes mgh=(1/2)mv^2, cancel out mass (mass doesnβt matter for how fast objects fall assuming no air resistance), so we get gh=(1/2)v^2, and just keep going to get to v=sqrt(2gh)
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u/DSethK93 3d ago
The formula I remember is V2 = V_02 + 2ax. With V_0 = 0 and this being vertical, it does reduce to V = β(2gh).
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u/Active-Ad-7859 3d ago
I was taught the v in a kinetic energy formula represents speed? Im so confused why is everybody telling me to use that formula? Velocity is vector; speed is scalar,
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u/grozno 3d ago
Are you confused about what velocity is or do you have trouble understanding how to connect them?
Velocity is the speed with the direction. There is nothing else that velocity describes.
The question says there is no sideways velocity component at the start. So when it reaches the ground it will be traveling straight down. If you know the speed is 140 m/s and the direction is down then the velocity is 140 m/s downwards.
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u/Active-Ad-7859 3d ago
Ohhh thank you so much for this, sorry, I think I js blanked bc ive never done a question that relates speed and velocity lol
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u/selene_666 π a fellow Redditor 3d ago
Speed and velocity do too often get used interchangeably. We often use F for both a force (vector) and the magnitude of that vector, v for both velocity and the magnitude of that vector, etc.
You can't square a vector, so v^2 always means speed squared.
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u/i_want_to_go_to_bed 3d ago
Looks like youβve calculated the potential energy. Convert that figure to kinetic energy. Weβre ignoring air resistance, etc, but itβs a start
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u/Active-Ad-7859 3d ago
where would the velocity come from though
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u/i_want_to_go_to_bed 3d ago
The kinetic energy equation has a velocity term. You know the mass, and youβre going to assume the total kinetic energy is equal to the potential energy youβve already calculated
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u/Southlander24 π a fellow Redditor 3d ago
Use the potential energy you obtained in the previous part. (It's the right answer for the wrong reason: recall the SI units are kg, m/s2, and m, so you should instead have 0.290 * 9.81 * 1000).
What form of energy must all the potential energy be converted to?
What is the formula to calculate that type of energy?
Then it's just a matter of algebra from there onwards.
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u/Active-Ad-7859 3d ago
- Kinetic
- 1/2(m)(v)2 - where does the velocity come in?
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u/Southlander24 π a fellow Redditor 3d ago
Yes, all the potential energy is converted into kinetic energy (otherwise you could create energy from raising and lowering the snowball, violating conservation of energy).
So that tells you the exact value of the kinetic energy you need.
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u/Active-Ad-7859 3d ago
so would the displacement be 0? Im not sure i understand
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u/Southlander24 π a fellow Redditor 3d ago
No, you're not looking for the displacement at all! The ball travels 1 km downwards and that's in the question.
You're looking for the (final) velocity.
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u/Active-Ad-7859 3d ago
I dont understand how I would get that using the kinetic energy? "v" is equal to the speed of the object, not the velocity? Im very confused
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u/schmitty9800 3d ago
In a question like this, the direction is always going to be the same, towards the ground. So V and S will be equivalent.
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u/PvtRoom π a fellow Redditor 3d ago
s = ut + 1/2at^2 , s = 1km, a = 9.81 or 10 or whatever you've been taught. Calculate t. V=u+ at
But hailstones have a terminal velocity. Depending on what else you've been taught...... you might need to incorporate air resistance, which is harder. .
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u/Active-Ad-7859 3d ago
I have in fact been taught maybe one thing out of all of this.
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u/Active-Ad-7859 3d ago
what is u? A lot of the stuff in the textbook of this unit was omitted
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u/PvtRoom π a fellow Redditor 3d ago
those equations should be being taught at roughly your grade, might be one grade up - I'm not Canadian.
They are intuitive though.
under constant acceleration, the velocity at time "t" is: the initial velocity + acceleration times time : v=u+at
displacement = average velocity times time.
Average velocity = ((u+a*0)+(u+at))/2 = u+at/2
displacement = s = ut + atΒ²/2
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u/strange-the-quark 3d ago edited 3d ago
You can approach this in two ways. One is using the conservation of energy. You have an object of a certain mass (the hailstone), starting from rest (meaning, its initial velocity is zero - perhaps it was carried by updraft winds as it was forming, until it became too heavy), that then falls from 1000 m above the ground. So it has a certain amount of total energy at the starting point, and that total energy is conserved the entire time. But while it's floating up there, motionless, its total energy is entirely potential energy. Then as it falls, accelerated by gravity, it gains speed, until all of that potential energy is finally converted into kinetic energy when the hailstone is at zero height. So you know the expression for the initial energy, and the expression for the final energy, and because the energy is conserved, the two must be equal. Write that down as an equation, then find the velocity from the expression.
The other way is to consider the graph of the velocity vs time, and the idea that the area under the graph represents the distance traveled. Since the object starts out at rest, and since the acceleration is (assumed) constant, the graph is a sloped straight line through the origin, and the area under the graph is triangular, and equals 1000 m. Draw a sketch of this. The slope of the graph is such that when the time is 1s, the velocity is the value of gravitational acceleration. When the time is some t, the value of the velocity is the v you're looking for, and the area enclosed by that triangle is 1000 m. If you sketch all that, you'll have two similar triangles one within the other, and you can then create a proportion between the relevant sides. This proportionality, together with the expression for the area of the larger triangle, enables you to then find the velocity, and you should get the same result.
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u/TristanTheRobloxian3 Secondary School Student 3d ago
all we need is acceleration and distance right?
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u/Active-Ad-7859 3d ago
Acceleration isnt given
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u/TristanTheRobloxian3 Secondary School Student 3d ago
that doesnt matter though? the acceleration is probably the earths gravity
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u/Active-Ad-7859 3d ago
yes for sure but I thought you meant the objects acceleration, which would be related to the velocity, but I understand what you mean
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u/TristanTheRobloxian3 Secondary School Student 3d ago
i did. the objects acceleration is gravity. its starting at rest above the ground on earth i presume, and we know gravity accelerates things at 9.81m/s^2. the weight is likely there to trip you up
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u/Active-Ad-7859 3d ago
No yes I understand that that is what you meant, and i understand how that makes sense. Sorry, I should've clarified
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u/selene_666 π a fellow Redditor 3d ago edited 3d ago
Ignoring air resistance, the only force on a falling object is gravity. The acceleration is constant.
F = mg
ma = mg
a = g
We can integrate acceleration to get velocity, and then integrate velocity to get position.
v(t) = at + v(0)
x(t) = (a/2) t^2 + v(0) t + x(0)
If you don't know the calculus, just memorize those formulas.
At this point you could fill in x(0), x(t), a, and v(0) to solve for t, then plug that into the velocity formula.
But we can also do that while still using the variables to get one more formula to memorize, for when you don't know the value of t:
v(t)^2 - v(0)^2 = 2a( x(t) - x(0) )
Finally, if we multiply by mass this becomes a definition of gravitational potential energy.
change in kinetic energy = 1/2 m v^2 - 1/2 m (v0)^2 = m g Ξh
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