"To reach the most distant planets such as Saturn and Uranus space probes require very great speeds. These space probes make use of the slingshot or gravity-assist effect. Would an observer on the assisting planet agree that the probe's speed has increased? Discuss your reasons."
No, the observer will argue that the probe's speed has not increased.
Relative to the observer, the probe's speed will appear to be unchanged. As the probe approaches the assisting planet, its GPE will decrease and its kinetic energy will increase but as the probe moves away from the assisting planet, its GPE will increase and kinetic energy will decrease relative to the observer. This means that the speed at which the probe approaches will be the same as the speed at which the probe moves away from the assisting planet.
In actual fact, the velocity of the probe
relative to the sun has changed in both magnitude and direction because the probe's output velocity is equal to the input velocity added to the velocity component of the assisting planet. This makes an observer from the sun argue that the probe's velocity (speed and magnitude) has increased.
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