A model rocket is initially a height of H = 2.00 m above the ground. At t = 0, it is released from rest and has its engines ignited. Its engines generate an acceleration in the positive y-direction which changes with time of magnitude ßt, where 3 = 18.00 m/s³. This acceleration doesn't include the effects of gravity. After 5.00 seconds have passed, the rocket's fuel will run out, and will no longer provide an upward thrust.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
 alt="A model rocket is initially a height of H = 2.00 m above the ground. At t = 0, it
is released from rest and has its engines ignited. Its engines generate an
acceleration in the positive y-direction which changes with time of magnitude ßt,
where = 18.00 m/s³. This acceleration doesn't include the effects of gravity.
After 5.00 seconds have passed, the rocket's fuel will run out, and will no longer
provide an upward thrust.
Q4.1 Part (a)
(a) Find the velocity and position of the rocket for all times t > 0.
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Q4.2 Part (b)
H+
(b) What is the maximum height the rocket will reach?
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Q4.3 Part (c)
(c) How long until the rocket returns to the ground?
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Q4.4 Part (d)
(d) What is the minimum height, H, necessary for the rocket to safely launch?
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