satellite is floating in space. Solar wind sweeping past the satellite consists of a stream of particles, mainly hydrogen ions of mass 1.7×10−27 kg. There are about 0.5×105 ions per cubic meter, and their speed is 8.0×105 m/s. An `umbrella' attached to the satellite is slowly opened, such that the radius of the circular cross-section of the umbrella is changing with time as r(t)=bt2, where b=0.1 m/s2 is a constant (see the figure which shows the side and front views). What is the maximum change of momentum of the satellite due to the solar wind hitting this umbrella after a time of 10 seconds? Explain carefully why this is the maximum possible change. You must explain your reasoning every step of the way!

satellite is floating in space. Solar wind sweeping past the satellite consists of a stream of particles, mainly hydrogen ions of mass 1.7×10−27 kg. There are about 0.5×105 ions per cubic meter, and their speed is 8.0×105 m/s. An `umbrella' attached to the satellite is slowly opened, such that the radius of the circular cross-section of the umbrella is changing with time as r(t)=bt2, where b=0.1 m/s2 is a constant (see the figure which shows the side and front views). What is the maximum change of momentum of the satellite due to the solar wind hitting this umbrella after a time of 10 seconds? Explain carefully why this is the maximum possible change. You must explain your reasoning every step of the way!