Thread: Algebraic Manipulation involving Trigonometry

In a certain collision problem the kinematics are determined by the following three equations.

u = v1cosθ + √(2)v2
v1sinθ = √(2)v2

1/2mu² = 1/2mv1² + 1/2(2m)v2²

Use the first two equations to express v1 and v2 in terms of u, sinθ and cosθ. Then substitute into the third equation and obtain solutions for sinθ.

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My working so far:

u = v1cosθ + v1sinθ
u = v1 (cosθ + sinθ )
v1 = u/(cosθ+sinθ )
v1² = u²/(cosθ + sinθ)²

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v1 = u/( sinθ + cosθ )
v1sinθ = √(2)v2
usinθ/( sinθ + cosθ ) = √(2)v2
u²sin²θ/( sinθ + cosθ )² = 2v2²
1/2[u²sin²θ/( sinθ + cosθ )²] = v2²

Are these two correct? and if so what should I do next?

Originally Posted by SunGod

In a certain collision problem the kinematics are determined by the following three equations.

u = v1cosθ + √(2)v2
v1sinθ = √(2)v2

1/2mu² = 1/2mv1² + 1/2(2m)v2²

Use the first two equations to express v1 and v2 in terms of u, sinθ and cosθ. Then substitute into the third equation and obtain solutions for sinθ.

--------------

My working so far:

u = v1cosθ + v1sinθ
u = v1 (cosθ + sinθ )
v1 = u/(cosθ+sinθ )
v1² = u²/(cosθ + sinθ)²

--------------

v1 = u/( sinθ + cosθ )
v1sinθ = √(2)v2
usinθ/( sinθ + cosθ ) = √(2)v2
u²sin²θ/( sinθ + cosθ )² = 2v2²
1/2[u²sin²θ/( sinθ + cosθ )²] = v2²

Are these two correct? and if so what should I do next?

I'll attached my suggested solutions as followed:

Thanks alot man, enjoy your positive rep.

You made a mistake, sin²@+1 does not equal cos²@

No matter I managed to fix it.