A scaffold elevator is moving up at a constant speed Ve = 2.0 m/s next to a tall building under construction as shown in the figure. The height of the building is h=100m. At the moment, the elevator passes the height d=20m, a ball is dropped from rest from the top of the building. After falling for some time, the ball strikes the floor of the elevator. Neglecting air resistance and assuming the acceleration due to gravity has a magnitude of 9.8 m/s2, determine the following From the moment it is released, how long does it take for the ball to strike the floor of the elevator? At what height from the base of the building is the elevator, when the ball strikes its floor? What is the speed of the ball when it strikes the elevator? On a single set of “y”, versus” t” axes, plot the graph of ye(t) and yb(t). That is, plot the graphs showing how the position of the elevator floor [ye(t)] and the position of the ball [yb(t)] change with time from the moment the ball is released. Indicate on your graph the moment the ball strikes the floor of the elevator.
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 scaffold elevator is moving up at a constant speed Ve = 2.0 m/s next to a tall building under construction as shown in the figure. The height of the building is h=100m. At the moment, the elevator passes the height d=20m, a ball is dropped from rest from the top of the building. After falling for some time, the ball strikes the floor of the elevator.
Neglecting air resistance and assuming the acceleration due to gravity has a magnitude of 9.8 m/s2, determine the following
- From the moment it is released, how long does it take for the ball to strike the floor of the elevator?
- At what height from the base of the building is the elevator, when the ball strikes its floor?
- What is the speed of the ball when it strikes the elevator?
- On a single set of “y”, versus” t” axes, plot the graph of ye(t) and yb(t). That is, plot the graphs showing how the position of the elevator floor [ye(t)] and the position of the ball [yb(t)] change with time from the moment the ball is released. Indicate on your graph the moment the ball strikes the floor of the elevator.
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