32. mmh Two rockets are flying in the same direction and are side by side at the instant their retrorockets fire. Rocket A has an initial velocity of +5800 m/s, while rocket B has an initial velocity of +8600 m/s. After a time t both rockets are again side by side, the displacement of each being zero. The acceleration of rocket A is –15 m/s2. What is the acceleration of rocket B?

 

The rockets are traveling in one direction when retrorockets fire which slow them down.  Eventually the retrorockets would bring the rockets to rest.  If the retrorockets are continuing to fire the rockets will begin to move in the opposite direction than they were originally.  They could arrive at the point in space in which the retrorockets were first fired.  At this point their net displacement would be zero.  If the acceleration is constant from the retrorockets, then  using the following equation

 

Since x = 0, the equation becomes

Solving for final velocity

This means at this point in space, there are two possible speeds, the original speed in the same direction and then at a later time the original speed again, only this time pointing in the other direction.  We can use this to solve for time which can then be used to find the other acceleration since the ships end up together both times.

 

Solving for time

Since we know

 

We get

Now apply to Rocket A

Now rearrange the equation to solve a and we can find the acceleration of Rocket B

 

 

 

Alternatively we could avoid solving for t by equating the two equations solving for t as follows:

Now solve for

 

 

 

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This page last updated on January 11, 2020