First dynamics question

>>7763588
The fuck is this?

Dynamics is supposed to be done with diffy Qs, not these high-school tier formulas.

Also step 4 you squared v2 but already took the root on the RHS. It should just be v2 without raising the power.

>>7763601
>Dynamics is supposed to be done with diffy Qs, not these high-school tier formulas.
First dynamics question, comrade
>Also step 4 you squared v2 but already took the root on the RHS. It should just be v2 without raising the power.
Thanks, I knew it would probably be something stupid asf

>>7763606
What the fuck... why did you use energy? This is literally high school Calculus. Fuck, not even. It's literally Algebra II; you don't need to know any physics to be able to understand/solve this problem.

I'll type out the work in just a second.

>>7763588
>>7763606
[math]y(t)=80t\sin(60)-\frac{1}{2}32.174t^2\\
x(t)=80t\cos(60)\\~\\
y(t)=40t\sqrt{3}-16.087t^2\\
x(t)=40t\\~\\
h=40t\sqrt{3}-16.087t^2\\
55+h=40t\\~\\
h\approx63.8397 ft \approx63.84 ft\\
t\approx2.97099 s \approx2.971s[/math]

And that's all. Nothing but a simple system of equations. All thanks to basic Algebra and a bit of Calculus/derivative knowledge.

>>7765083
Let me try reformatting that...

[eqn]
y(t)=80t\sin(60)-\frac{1}{2}32.174t^2\\
x(t)=80t\cos(60)\\
y(t)=40t\sqrt{3}-16.087t^2\\
x(t)=40t\\
h=40t\sqrt{3}-16.087t^2\\
55+h=40t\\
h\approx63.8397 ft \approx63.84 ft\\
t\approx2.97099 s \approx2.971s
[/eqn]

File: work.png (14KB, 242x271px)

14KB, 242x271px

>>7765083
>>7765084
>>7763588
>>7763606
Fuck it, I'm just going to upload it as a picture. You're welcome.

>pic related

>>7763601

m8, linear Diffy Q's can be reduced down to simple algebra.

>>7763588
>> 2016
>>>using the flat earth approximation and treating the atmosphere as a vacuum to calculate the trajectory of a projectile

>>7765084
the latex here is brain damaged
it'll work if you put a lot of white space around the commands

[eqn]
y(t)=80t \sin(60)-\frac{1}{2} 32.174 t^2 \\
x(t)=80t \cos(60) \\
y(t)=40t \sqrt{3} - 16.087 t^2 \\
x(t)=40t \\
h=40t \sqrt{3}-16.087t^2 \\
55+h=40t \\
h \approx 63.8397 ft \approx 63.84 ft \\
t \approx 2.97099 s \approx 2.971s
[/eqn]

>>7763601
>Dynamics is supposed to be done with diffy Qs, not these high-school tier formulas
You're that cunt who likes to lord his slightly more advanced classes over the younger students to give the impression that he is smarter than they are because they're still in first year mechanics while he knows all about the much deeper physics of second year mechanics. I remember students like you.

>>7765083
>>7765084
>>7765090
Let this thread die already, this >>7763601 guy answered the question

>>7765177
bump

>>7765166
No you fucking mongoloid. "Dynamics" by definition refers to time dependents DEs. That is why using an energy balance defeats the entire purpose of the introductory exercise.

No one thinks calc is advanced, just shut the fuck up with your stupid assumptions.

Stop implying you've graduated high-school either, you would know what dynamics was if you did.