Answer to Question #5198 in Mechanics | Relativity for Brittany
Let x be the position of their docking and t is
time needed to arrive to the x.
Let the first spacecraft started from the
position 0 and let X-axis be directed from the first spacecraft to the
Then we have that the second spacecraft starts from the position
Let's write a system of equations for displacements and velocities, as
we know that their final velocities must be zeroes:
x = V1*t -
x = 13500 - V2*t + (a2*t^2)/2,
V1 - a1*t = 0,
V2 - a2*t =
From the third and the 4th equations we get
t = V1/a1,
V1 * a2/a1.
When we substract the second equation from the first, we
0 = V1*t - (a1*t^2)/2 - 13500 + V2*t - (a2*t^2)/2,
0 = V1*V1/a1 - (a1*(V1/a1)^2)/2 - 13500 + V1 * a2/a1*V1/a1 -
0 = V1^2/(2*a1) - 13500 + (a2*(V1/a1)^2)/2,
a1 - 27000*(a1/V1)^2 + a2,
a2 = 27000*(a1/V1)^2 - a1,
27000*(15.5/525)^2 - 15.5 = 8,
V2 = V1 * a2/a1 = 525*8/15.5 =
So, the second spacecraft has initial velocity 271 m/s directed
toward the first spacecraft and acceleration -8 m/s^2.
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