glx) = -0.04x2 + 2.1x + 6.1 Shot released at 65° 40 Maximum height 30 Maximum height Distance of throw or maximum horizontal distance 10 flx) = -0.01x2 + 0.7x + 6.1 Shot released at 35° 10 20 30 40 50 60 70 80 90 Shot Put's Horizontal Distance (feet) Shot Put's Height (feet) 20
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.
An athlete whose event is the shot put releases the shot with the same
initial velocity but at different angles. The figure shows the parabolic paths for shots released at angles of 35° and 65°. Solve the following based on the functions that model the parabolic paths.
When the shot whose path is shown by the red graph is released at an angle of 65°, its height, g(x), in feet, can be modeled by g(x) = -0.04x2 + 2.1x + 6.1, where x is the shot’s horizontal distance, in feet, from its point of release. Use this model to solve the below parts (a) through (c) and verify your answers using the red graph.
a. What is the maximum height, to the nearest tenth of a foot, of the shot and how far from its point of release does this occur?
b. What is the shot’s maximum horizontal distance, to the nearest tenth of a foot, or the distance of the throw?
c. From what height was the shot released?
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