A student walks off the top of the CN Tower in Toronto, which has height 553 mm and falls freely. His initial velocity is zero. The Rocketeer arrives at the scene a time of 5.50 ss later and dives off the top of the tower to save the student. The Rocketeer leaves the roof with an initial downward speed v0v0. In order both to catch the student and to prevent injury to him, the Rocketeer should catch the student at a sufficiently great height above ground so that the Rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by the Rocketeer's jet pack, which he turns on just as he catches the student; before then the Rocketeer is in free fall. To prevent discomfort to the student, the magnitude of the acceleration of the Rocketeer and the student as they move downward together should be no more than five times gg. 1)What is the minimum height above the ground at which the Rocketeer should catch the student? 2)What must the Rocketeer's initial downward speed be so that he catches the student at the minimum height found in part (a)?
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.
A student walks off the top of the CN Tower in Toronto, which has height 553 mm and falls freely. His initial velocity is zero. The Rocketeer arrives at the scene a time of 5.50 ss later and dives off the top of the tower to save the student. The Rocketeer leaves the roof with an initial downward speed v0v0. In order both to catch the student and to prevent injury to him, the Rocketeer should catch the student at a sufficiently great height above ground so that the Rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by the Rocketeer's jet pack, which he turns on just as he catches the student; before then the Rocketeer is in free fall. To prevent discomfort to the student, the magnitude of the acceleration of the Rocketeer and the student as they move downward together should be no more than five times gg.
1)What is the minimum height above the ground at which the Rocketeer should catch the student?
2)What must the Rocketeer's initial downward speed be so that he catches the student at the minimum height found in part (a)?
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