An example of an elastic collision is The gravitational slingshot effect . A spacefship of mass 750 kg is moving at 12.5 km/s in the +x direction. It approaches the planet Saturn, mass 5.68 x10 26kg , which is moving in the –x- direction as shown in the figure. The gravitational attraction of Saturn accelerates the spaceship as it approaches and causes to swing around the planet and heads off in the same direction as Saturn. Several probes such as Voyager have used this to save on “gas”. Estimate the final speed of the spacecraft after it is far enough to be considered free of Saturn’s gravitational pull. Assume that the speed of Saturn is not affect due to its large mass. Express your answer in km/s. HINT: perfectly ELASTIC COLLISION. The image illustrates a spacecraft performing a gravitational assist maneuver around a planet, which resembles Saturn. The spacecraft's trajectory is depicted as a dashed line, indicating its path as it approaches and moves away from the planet.Key elements shown in the diagram include:1. **Spacecraft Path**: - The spacecraft is shown approaching the planet with an initial speed labeled \(v_{Sp}\) (approach speed of spacecraft). - The path curves around the planet, following a hyperbolic trajectory.2. **Planet's Velocity**: - The planet has a velocity denoted as \(v_S = -9.6 \text{ km/s}\), indicating its motion in the opposite direction of the spacecraft's initial approach.3. **Unknown Speed After Assist**: - The spacecraft's speed after the gravitational assist is labeled as \(v'_{Sp} = ?\), representing the unknown final speed of the spacecraft after the maneuver.4. **Coordinate System**: - An arrow labeled \(x\) indicates the direction of the coordinate axis, helping to establish the frame of reference for the velocities.This diagram is typically used to explain the concept of gravitational slingshot or gravity assist, where a spacecraft gains additional speed and alters its trajectory by passing close to a massive body like a planet.

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A spacefship of mass 750 kg is moving at 12.5 km/s in the +x direction. It approaches the planet Saturn, mass 5.68 x10 26kg , which is moving in the –x- direction as shown in the figure. The gravitational attraction of Saturn accelerates the spaceship as it approaches and causes to swing around the planet and heads off in the same direction as Saturn. Several probes such as Voyager have used this to save on “gas”. Estimate the final speed of the spacecraft after it is far enough to be considered free of Saturn’s gravitational pull. Assume that the speed of Saturn is not affect due to its large mass.

A spacefship of mass 750 kg is moving at 12.5 km/s in the +x direction. It approaches the planet Saturn, mass 5.68 x10 26kg , which is moving in the –x- direction as shown in the figure. The gravitational attraction of Saturn accelerates the spaceship as it approaches and causes to swing around the planet and heads off in the same direction as Saturn. Several probes such as Voyager have used this to save on “gas”. Estimate the final speed of the spacecraft after it is far enough to be considered free of Saturn’s gravitational pull. Assume that the speed of Saturn is not affect due to its large mass.

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