# Find the angle so that it seems that Mars is approaching to you

#### Like Tony Stark

Homework Statement
The spaceship S approaches Mars following the trajectory $b−b$ with velocity $19.3 km/s$ with respect to the Sun. If Mars has a velocity $24.1 km/s$ along the trajectory $a−a$ with respect to the Sun and the angle between $b-b$ and $a-a$ is $30°$ determine the angle between $SM$ and $b−b$ such that a person inside the spaceship "sees" that Mars is moving towards him
Homework Equations
$v_{M/S}=v_M - v_S$.
I know that $v_{M/S}=v_M - v_S$. I also know that $v_M = (-24.1;0)$. Then, using some trigonometry, $v_S=(-19.3 sin 30°;19.3 cos 30°)$.
So I can find $v_{M/S}$. But that doesn't tell me anything about the angle $\beta$.

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#### mfb

Mentor
You have all three sides of a triangle, you can find the angles.

#### Like Tony Stark

You have all three sides of a triangle, you can find the angles.
What triangle are you talking about? The one formed by the $v_S$, $v_M$ and $v_{M/S}$?

#### mfb

Mentor
Yes. The time until you and Mars collide is fixed, so distances and velocities are proportional to each other.

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