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Find x(t), y(t), z(t), vx(t), vy(t), vz(t) for a projectile in 3-D with air resistance and...

Find x(t), y(t), z(t), vx(t), vy(t), vz(t) for a projectile in 3-D with air resistance and wind resistance.

Given: vector for vo=(vx,vy,vz), vector for wind vw=wŷ

Equation of motion of projectile: Ftot=ma=-my(z-hat)- β(vector for vo)+ β(vector for vw)y

Science   Advanced-Physics   
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Homework Answers

Answer #1

... (1)

Subst,

we get, comparing the x, y, z part of the differential eqn (1),

...(2)

...(3)

...(4)

(2), (3) and (4) are the linear ordinary differential equations.

Solving (2),

...(5)

Solving (3),

...(6)

Solving (4),

...(7)

where C1, C2, C3 are constants which can be evaluated if initial conditions are given.

Now, solving (5),

Similarly, solving (6) we get,

Solving (7),

Here D1 , D2 , D3 are constants which can be evaluated given initial conditions.

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