Please answer this with the explanation. Thank you. As of September, 2017, NASA\
ID: 1654671 • Letter: P
Question
Please answer this with the explanation. Thank you.
As of September, 2017, NASA's Dawn spacecraft is nearing the end of its decade-long mission. You can read more about it here. It orbited two protoplanets (Vesta and Ceres) in the asteroid belt, between Mars and Jupiter, sending back plenty of excellent photos. The Dawn spacecraft was the first spacecraft to rely on ion propulsion. Ions are accelerated by high voltage to high speeds, propelling the spacecraft in the opposite direction. The acceleration can be rather small. Let's say that the spacecraft accelerates from rest to 60 miles per hour over a time period of 4 days. Assuming the acceleration is constant, what is the magnitude of the acceleration? m/s/s (b) Despite this small acceleration, fairly high speeds can be reached, and significant distances covered, by having the spacecraft accelerate for a long time. How far would Dawn travel, starting from rest, with the acceleration above taking place for 840 days? mExplanation / Answer
(a) First convert 60 miles per hour in meter per sec.
60 mile per hour = 26.8 m/s. = v
time, t = 4 days = 4 x 24 x 60 x 60 sec = 345600 s.
now use the expression -
v = u + a*t
spacecraft starts from rest. so u = 0
put the values-
26.8 = 0 + 345600 * a
=> a = 7.75 x 10^-5 m/s/s
(b) here, t = 840 days = 840 x 24 x 60 x 60 sec.
So, distance covered by the spacecraft in this time -
s = u*t + (1/2)*a*t^2 = 0 + 0.5 x 7.75x10^-5 x (840 x 24 x 60 x 60)^2 = 2.041 x 10^11 meter.