A hovercraft has an initial position of r(t = 0s) = 235m @ 265◦, an initial velocity of ⃗v(t = 0s) = 125m/s @ 14◦, and a constant acceleration of ⃗a = 21.3m/s^2 @ 143◦ . (a) How long does it take for the x coordinate of the hovercraft’s position to reach -100m? (b) What is the hovercraft’s position at this time? (c) What is the hovercraft’s velocity at this time?
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 hovercraft has an initial position of r(t = 0s) = 235m @ 265◦, an initial velocity of
⃗v(t = 0s) = 125m/s @ 14◦, and a constant acceleration of ⃗a = 21.3m/s^2 @ 143◦
.
(a) How long does it take for the x coordinate of the hovercraft’s position to reach -100m?
(b) What is the hovercraft’s position at this time?
(c) What is the hovercraft’s velocity at this time?
i = (t=0s)235
=235[-sin-cos]
=[-20.48-234.11]m
=125[cos14+sin14]
=[121.29+30.24]m/s
= 21.3[-cos37+sin37]
=[-17.01+12.82]m/s2
b) using second equation of motion
(rxf -rxi ) =uxt+1/2axt2
-100+20.48 = 121.29t-1/2*17.01t2
-79.52 = 121.29t =-8.535t2
t2 -14.21t-9.317 =0
t = 14.21/2*1
=7.1057.733
=14.84s
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