UP Us Sending spaceships to the outer regions of the solar system requires large energies. The slingshot effect is a frequently used method for speeding up spaceships without using much rocket fuel. To use this effect, the spaceship is diverted to pass around one of the inner planets (such as Venus). If the spaceship is sent in the right direction, it will reach to greater speeds after it passes around the planet. You will see the effect at play in this question. A spaceship is sent with an initial velocity of vs = (15 j+ 30 i) km/s towards a planet. The planet is moving with velocity vp = 50i km/s. After the encounter with the planet, the spaceship emerges to be moving along the +x direction (with a final velocity of the form s = vg i). Find the final speed of the spaceship in units of km/s. U's km/s. %3D Hint 1: This is an elastic "collision". When you hear the word collision, you usually imagine something that happens quickly; in contrast this collision happens over days and perhaps even weeks. But, you can use the same equations to treat all. Hint 2: (This is really unnecessary to state, but sometimes I am obliged to state the obvious): Assume that the mass of the planet is much larger than the mass of the spaceship.

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