Problem 4: A catapult launches a test rocket vertically upwards from a well, giving the rocket an initial speed of 80 m/sec at ground level. The engines then fire, and the rocket accelerates upward at 4 m/sec² until it reaches an altitude of 1000 m. a) How long does it take the rocket to reach the altitude of 1000 m? Answer: 10 sec b) What is the speed of the rocket when it reaches an altitude of 1000 m? Answer: 120 m/sec Time t y 1000 m. t=0 Yo=0- Vo = 80 m/sec a = 4 m/sec² Engines On Vo ¯†à v = 0 m/sec When the rocket reaches an altitude of 1000 m, the engines fail and the rocket goes into free fall, with an acceleration of a = -g. For the remainder of this problem, the rocket engines will be off. We will re-define t = 0 sec to be the time when the rocket is at an altitude of 1000 m. The initial properties of the rocket will be the properties of the rocket at 1000. c) What is the largest height the rocket reaches? Answer: 1734.7 m d) What is the time it takes the rocket to hit the ground? Answer: 31.06 sec e) What is the velocity of the rocket just before it hits the ground? Answer: -184.4 m/sec AY Engines Off
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.
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