58 683
Assignments Done
Successfully Done
In March 2018
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Mechanics | Relativity Question for Brittany

Question #5198
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. What would the average acceleration of the second spacecraft be in m/s2? Hint: Use the first spacecraft to get needed information for the second spacecraft remembering that the time is the same for both and their total distance is 13,500 m. Assume the second spacecraft to have a positive initial velocity. Include a sign with your answer.
Expert's answer
Let V1, V2, a1, a2 - velocities and accelerations of the first and the second
spacecrafts respectively.
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,
V2 =
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,

0 =
a1 - 27000*(a1/V1)^2 + a2,

a2 = 27000*(a1/V1)^2 - a1,

a2 =
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.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be first!

Leave a comment

Ask Your question