A rocket can produce any acceleration up to a maximum magnitude of 64 m/s2 without breaking apart. The rocket starts at rest, and wishes to arrive at rest at a location 3,190 m away in as little time as possible. When the rocket's position is x, its acceleration is a(x), where a(x) can take any form (continuous or discontinuous) so long as |a(x)| ≤ 64 m/s2 always. What is the minimum amount of time the journey can take, in s?
A rocket can produce any acceleration up to a maximum magnitude of 64 m/s2 without breaking apart. The rocket starts at rest, and wishes to arrive at rest at a location 3,190 m away in as little time as possible. When the rocket's position is x, its acceleration is a(x), where a(x) can take any form (continuous or discontinuous) so long as |a(x)| ≤ 64 m/s2 always. What is the minimum amount of time the journey can take, in s?
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Question
A rocket can produce any acceleration up to a maximum magnitude of 64 m/s2 without breaking apart. The rocket starts at rest, and wishes to arrive at rest at a location 3,190 m away in as little time as possible. When the rocket's position is x, its acceleration is a(x), where a(x) can take any form (continuous or discontinuous) so long as |a(x)| ≤ 64 m/s2 always. What is the minimum amount of time the journey can take, in s?
(Please answer to the fourth decimal place - i.e 13.2332)
Expert Solution
Step 1
Given:
acceleration of the rocket, a(x) = 64 m/s2 (for minimum time)
distance travelled, S = 3,190 m
initial velocity, u = 0 m/s
final velocity, v = 0 m/s
Determine the minimum time taken to cover the distance S.
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