Question

A space craft, mass 100 ?? is in outer space at location < 1, 2, 5 > ? moving at an initial speed of 2 ?/? One set of thrusters are now turned on and exert a constant force < −100, 200, 0 > ? until the object reaches location < 2, 3, 5 > ?. At this point, these thrusters are turned off, and another set of thrusters are turned on which exert a constant force < 200 − 100,0 > ? until the space craft reaches < 5,4,5 > ?.

What is the speed of the space craft at the final location?

Answer 1

magntiude of force |F| due initial thrust is given by

acceleration = 223.61/100 = 2.236 m/s2

displacement s is given by

if initial speed is 2 m/s , final speed is obtained from the equation of motion

" v2 = u2 + 2 a S "

where v is speed due to initial thrust,

u = 2 m/s is initial speed, a = 2.236 m/s2 is acceleration

and S = m is displacement .

v2 = 4 + 2 (2.236) (1.414) = 10.323

v = 3.213 m/s

magntiude of force |F| due second thrust is given by

acceleration = 223.61/100 = 2.236 m/s2

displacement s is given by

final speed is obtained from,

v2 = (3.213)2 + 2 ( 2.236) = 24.465

final speed v = 4.95 m/s