# First

`a(t) = < 0, 0.36, -9.8 >`
`∫a(t) = v(t) = < 0, 0.36t, -9.8t > + 𝘾`
`<300cos(30), 0, 300sin(30)>simplifies to => <150√(30), 0, 150>, this is 𝘾!`
`<150√(30), 0, 150> + < 0, 0.36t, -9.8t >Our Velocity function => v(t) = <150√(30), 0.36t, -9.8t + 150 >`
`∫v(t) = r(t) = <150√(30)t, 0.18t², -4.9t² + 150t> + 𝘾`
`Position function => r(t) = <150√(30)t, 0.18t², -4.9t² + 150t>`
`-4.9t² + 150t = 04.9t² = 150t4.9t = 150t = 150/4.9 <= this, in seconds, is when our projectile hits the    ground!`
`t = 150/4.9r(t) = <150√(30)t, 0.18t², -4.9t² + 150t>r(150/4.9) = <150√(30)(150/4.9), 0.18(150/4.9)²>solving both components:Xdistance ≈ 7953.294525Ydistance ≈ 168.6797168`
`totalDistance = √(7953.294525)² + (168.6797168)²totalDistance ≈ 7955.08307m `

# NOW LETS WRITE IT IN PYTHON:

`180° = 𝜋=> 1°= 𝜋/180We were given 30° so:30°𝜋/180simplifies to => 𝜋/6`
`from sympy.vector import CoordSys3Dfrom sympy import *N = CoordSys3D('N')myVector = N.i + 10*N.kmyVector is a Vector pointing from the origin to the point (1,0,10)(N.i means i)`
`myFunction = integrate(Function, x) "integrate the function called "function" with respect to x"`

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## More from Jack Callaway Sanders

A Fullstack Web Dev-arino, part time ‘cool guy’. My website is https://jacksanders.xyz

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## Jack Callaway Sanders

A Fullstack Web Dev-arino, part time ‘cool guy’. My website is https://jacksanders.xyz