Answer:
The acceleration required by the rocket in order to have a zero speed on touchdown is 19.96m/s²
The rocket's motion for analysis sake is divided into two phases.
Phase 1: the free fall motion of the rocket from the height 2.59*102m to a height 86.9m
Phase 2: the motion of the rocket due to the acceleration of the rocket also from the height 86.9m to the point of touchdown y = 0m.
Explanation:
The initial velocity of the rocket is 0m/s when it started falling from rest under free fall. g = 9.8m/s² t1 is the time taken for phase 1 and t2 is the time taken for phase2.
The final velocity under free fall becomes the initial velocity for the accelerated motion of the rocket in phase 2 and the final velocity or speed in phase 2 is equal to zero.
The detailed step by step solution to the problems can be found in the attachment below.
Thank you and I hope this solution is helpful to you. Good luck.
I believe it's the the third one. :)
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To solve the problem, it is necessary to apply the concepts related to the kinematic equations of the description of angular movement.
The angular velocity can be described as
Where,
Final Angular Velocity
Initial Angular velocity
Angular acceleration
t = time
The relation between the tangential acceleration is given as,
where,
r = radius.
PART A ) Using our values and replacing at the previous equation we have that
Replacing the previous equation with our values we have,
The tangential velocity then would be,
Part B) To find the displacement as a function of angular velocity and angular acceleration regardless of time, we would use the equation
Replacing with our values and re-arrange to find 
That is equal in revolution to
The linear displacement of the system is,
The speed of sound depends on the medium in which it is transported.
Sound travels fastest through solids, slower through liquids and slowest through gases.
So it will travel slowest through water at 55 degrees
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