Dawn is a space probe launched by NASA in September 2007 with the mission of stu

Question

Dawn is a space probe launched by NASA in September 2007 with the mission of studying two of the three known protoplanets of the asteroid belt. Vesta and Ceres. It is currently in orbit About its second target, the dwarf planet Ceres. Dawn entered Vesta orbit on July 16, 2011, and completed a 14-month survey mission before leaving for Ceres in late 2012. Dawn entered Ceres orbit on March 6, 2015, and is predicted to remain in orbit perpetually after the conclusion of its mission e Dawn mission is managed by NASA's Jet Propulsion Laboratory, with spacecraft components contributed by European partners from the Netherlands, Italy and Germany. It is the first NASA exploratory mission to use ion propulsion, which enabled it to enter and leave the orbit of multiple celestial bodies. Dawn's ion propulsion system uses a -1300 Volt potential difference generated by solar panels to ionize and accelerate Xenon gas from rest. Given this potential difference, how fast are singly ionized Xenon atoms traveling when they leave the engine? Xenon atoms have a mass of 2.18 Times 10^-25 kg.

Explanation / Answer

V = Potential difference = 1300 volts

q = charge = 1.6 x 10-19 C

m = mass = 2.18 x 10-25 kg

Using conservation of energy

kinetic energy = electric potential energy

(0.5) m v2 = qV

(0.5) (2.18 x 10-25 ) v2 = (1.6 x 10-19 ) (1300)

v = 4.4 x 104 m/s

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