+16 Two spacecraft are 13,500 m apart and moving directly toward each other. The first spacecraft has velocity 525 m/s and accelerates at a constant −15.5 m/s2. They want to dock, which means they have to arrive at the same position at the same time with zero velocity. (a) What should the initial velocity of the second spacecraft be in m/s? (b) What should be its constant acceleration in m/s2?
+37103 Craft One reaches zero velocity when?
v=vo + at = 525 + (-15.5)t = 0 Solve for t = 33.87 sec
How far did it travel in 33.87 secs?
x = xo + vo t + 1/2a t^2
x= 0 + 525(33.87) + 1/2(-15.5)(33.87)^2 = 8891.13 meters
Craft 2 has to cover 13500 meters - 8891.13 meters = 4608.87 meters i the same amount of time (33.87 seconds)
FOR CRAFT 2 :
x = xo + vo t + 1/2 a t^2 and
v = vo + a t = 0 or a t = -vo substitute into the equation above
4608.87 = 0 + vo (33.87) + 1/2 (-vo)(33.87) results in vo = 272.15 m/s
then vf = vo + a t = 272.15 + a (33.87) = 0 a= -8.04 m/s^2
+37103 Craft One reaches zero velocity when?
v=vo + at = 525 + (-15.5)t = 0 Solve for t = 33.87 sec
How far did it travel in 33.87 secs?
x = xo + vo t + 1/2a t^2
x= 0 + 525(33.87) + 1/2(-15.5)(33.87)^2 = 8891.13 meters
Craft 2 has to cover 13500 meters - 8891.13 meters = 4608.87 meters i the same amount of time (33.87 seconds)
FOR CRAFT 2 :
x = xo + vo t + 1/2 a t^2 and
v = vo + a t = 0 or a t = -vo substitute into the equation above
4608.87 = 0 + vo (33.87) + 1/2 (-vo)(33.87) results in vo = 272.15 m/s
then vf = vo + a t = 272.15 + a (33.87) = 0 a= -8.04 m/s^2
